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1. Mate of the Art in Wa r raeetton Analyres USER MANUAL it 2 1 4 2 3 4 a BO TES NCPU WAMIT INC TIME min D www wamit com WAMIT USER MANUAL Version 7 1 This User Manual has been prepared for users of WAMIT Version 7 1 WAMIT is distributed by WAMIT Inc under a special agreement with the Massachusetts Institute of Technology Further information is available from the website shown below The WAMIT software and this User Manual are Copyrighted by WAMIT Inc and by the Massachusetts Institute of Technology The User Manual can be downloaded from the website without a license WAMIT Inc 822 Boylston St Suite 202 Chestnut Hill MA 02467 2504 USA phone 617 739 4488 fax 617 739 4499 www wamit com 0 1 Copyright 1998 2015 WAMIT Incorporated and Massachusetts Institute of Technology No part of the WAMIT software or documentation may be reproduced translated or transmitted in any form without the express written permission of WAMIT Inc WAMIT is a registered trademark of WAMIT Inc Intel is a registered trademark of Intel Corporation Windows is a registered trademark of Microsoft Corporation MultiSurf and RGKernel are registered trademarks of AeroHydro Inc Tecplot is a registered trademark of Amtec Engineering Inc 0 2 TABLE OF CONTENTS 1 INTRODUCTION N w Aa LA 12 1 3 2 1 2 2 2 3 2 4 2 5 2 6 Bal 2 8 2 9 3 1 3 2 3 3 3 4 3 5 3 6
2. Each test run is described briefly in the following sections Also included in these sections are perspective illustrations of the complete underwater geometry including re flections about the indicated planes of symmetry and abbreviated listings of the input files For the low order tests the perspective figures show the subdivisions into panels For the higher order tests two perspective figures are included to show the subdivisions into patches upper or left and into panels lower or right All of the required input files for each test run and the labeled output file out are included with the WAMIT software provided to licensed users The same files can be downloaded with the demonstration programs from the web site http www wamit com The input files for Test Run tst are named with the filename testtst followed by the extensions gdf pot and frc The corresponding files fnames and config are given the same filenames with the extensions wam and cfg The additional configuration file config wam is included with the test files and is intended to supplement the separate cfg file for each test The standard version of this file is as shown below generic configuration file config wam RAMGBMAX 0 5 NCPU 1 USESRID PATH c lwamitv7 The first line is a comment line which is ignored by the program The parameters on the other lines are explained in Section 4 7 Before running TESTtst the user should copy the fn
3. The first four lines of the GDF are the same as in other optional GDF formats header ULEN GRAV ISX ISY NPATCH IGDEF Where header is an identifying character string up to 72 chars ULEN is a characteristic length GRAV is acceleration due to gravity ISX ISY are symmetry flags 0 or 1 for X and Y mirror symmetry NPATCH number of surfaces in this body not counting X and Y mirror symmetry images but counting Z axis rotational symmetry images Starting with WAMIT v 6 4 NPATCH can be specified as 0 see discussion below IGDEF 2 for using geometry from an MS2 file In an GDEF 2 GDF file there are always 4 more lines Line 5 NLINES number of lines to follow this line 3 plus number of parameter lines Line 6 Mode filename including extension MS2 no embedded spaces Line 7 Name of Entity List to be present in the named M S2 file listing the wetted surfaces Alternative use to signify all visible surfaces and make sure only the wetted surfaces are visible in your model when the M S2 file is saved Optionally line 7 can additionally havea second Entity List name specifying internal tank surfaces Line 8 3 integers Fast accurate flag 0 fast 1 accurate Divisions multiplier override 0 to 10 A 0 for DivMult will mean use the value in the model file Inward normal flag 0 outward normals 1 inward normals Then there are NLINES 3 optional parameter lines each with 3 items
4. 0000000E 00 8772585E 02 7835436E 02 0000000E 00 0000000E 00 7835436E 02 TESTO5 FRC Cylinder spheroid ILOWHI 0 1 1 1 1 0 test0bc frc test05s fre 0 1 0 0 0 3 1 1 Input file test05c frc CYL FRC 0 0 0 0 0 0 0 0 0 0 000000 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 0 0 Input file test05s frc SPD FRC 0 0 0 0 0 0 0 0 0 0 000000 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 0 0 First 10 lines of input file test05c csf cylinder R 1 2 T 2 2 low order control surface 0 ILOWHICSF 1 1 ISX ISY 160 NPAN 12000E 01 0 00000E 00 0 00000E 00 12000E 01 00000E 00 0 27500E 00 11769E 01 23411E 00 0 27500E 00 11769E 01 23411E 00 0 00000E 00 11769E 01 23411E 00 0 00000E 00 11769E 01 23411E 00 0 27500E 00 Oo 0000 Ooo 0 0oo Input file test05s csf ELLIPSOID CONTROL SURFACE defined by subroutine ELLIPSOID CS 1 ILOWHICSF 1 1 ISX ISY 1 1003 0 5 NPATCH IGDEF PSZCSF 2 NLINES 2 2 0 3 0 3 A B C 2 0 0 25 x and y maximum of ellipsoid GDF Input file test05a cfg TESTOS5a CFG array of field points IPLTDAT 1 ISOR 1 ILOG 0 IRR 0 NUMHDR 1 NOOUT 0 11101111 IALTFRC 3 Alternative Form 3 FRC IALTFRCN 1 1 IFIELD ARRAYS 1 Input file test05a pot TESTO5a POT Cylinder spheroid ILOWHI 0 1 0 HBOT Oo 0 IRAD IDIFF 2 NPER 1 5 2 0 PER 1 NBETA 90 0 Beta
5. 2 0 15 16 where Jo x is the Bessel function of zero order In finite depth the Green function is defined by 15 3 k K coshk z H coshk H sh ksinhkH K coshkH Jo kR 15 17 Gag 542 ak fy wn esac 28 15 18 In both expressions 15 14 and 15 17 the Fourier k integration is indented above the pole on the real axis in order to enforce the radiation condition Efficient algorithms for the evaluation of the infinite and finite depth wave source potentials and their spatial derivatives have been developed in 1 and 11 Special attention must be given to the singular components of the Green function for small values of r r and r The source like singularities 1 r 1 r and 1 r and their normal derivatives can be integrated analytically over a quadrilateral panel as described in 2 In addition the ascending series expansion of the wave source potential for small values of r Ref 1 eq 5 reveals the presence of the logarithmic singularity G x 45 2K log K z 00 15 19 The derivation of this result in 1 is for the infinite depth case but it can be shown from the analysis of the finite depth case in the same reference that the same singularity applies Provision has been made in WAMIT to permit the logarithmic singularity and its derivatives to be integrated analytically in the solution of the integral equations when the source and field point
6. EXMASS 2 6 NEWMDS EXMASS 6 NEWMDS 1 EXMASS 6 NEWMDS 2 EXMASS 6 NEWMDS 6 NEWMDS For N interacting bodies the number of data in MASS are NDFR x NDFR where NDFR 3 _ 6 NEWMDS n is the total number of rigid body modes and generalized modes Similarly the external damping and stiffness can be specified to the files DAMP and STIF In summary there are three legal values for IMASS IDAMP ISTIFF I 0 no matrix or file name is input matrix is assumed equal to zero I 1 matrix follows on subsequent lines I 2 file name follows on next line The procedure to designate Alternative Form 2 is to assign the parameter IALTFRC 2 in the configuration file as described in Section 4 7 and use the formats above In early versions of WAMIT the parameter IALTFRC was assigned differently by inserting the integer 2 on a separate line after the header line of the FRC file This variant of the FRC file format was supported in Version 6 Version 7 issues an error message if this variant is input 4 5 DEFINITION OF FIXED OR FREE MODES It is possible to specify that a sub set of the modes of body motion analyzed in POTEN can be fixed in FORCE As a simple example consider a single body with six degrees of rigid body motions all of which have been analyzed in POTEN either by setting IRAD 1 or by setting IRAD 0 and setting all six elements of MODE 1 Normally in the FORCE analysis if IOPTN 4 gt 0 the body motions are computed for all deg
7. If this file does not exist or if it is incomplete the user is prompted to supply the missing filenames interactively The number and order of these filenames is arbitrary In Version 7 the GDF filename s are specified in the POT file and it is not necessary to specify any GDF filename in the FNAMES file The only lines which are significant in the fnames wam file are those which contain an ASCII string ending in cfg pot or fre Thus comment lines can be inserted as long as they do not include one of these three strings 4 9 FILE NAMES The names of the input data files must not exceed 20 characters in length including ex tensions and including one period separating the filename and extension Filenames cannot include intermediate blank spaces white spaces Provisions are made in WAMIT to guard against unintended loss of old output files depending on the configuration parameters IDELFILES and IOUTFNAME In the default case where these parameters are not used or are equal to zero and if the names specified for the P2F and OUT files are identical to existing files the user is prompted interactively to choose between 1 changing the new output filename or 2 overwriting the old file If a new filename is specified interactively it must include the desired extension For example if the name test01 frc is retained as described in Section 2 9 instead of a modified name such as test0O1x frc the use
8. 13 5 One extra output file is produced with the extension _KR 1 containing the impulse response functions K which are defined in Reference 30 These alternative IRF s are evaluated in F2T by numerical differentiation of the IRF s L and can be used with a similar convolution integral as in 13 1 but using the velocity j instead of the acceleration gj The diffraction files _JR are different from the radiation files in two respects to facilitate their use First the time steps begin with NT xDT and end with NTxDT Secondly the cosine and sine transforms are combined adding for t lt 0 and subtracting for t gt 0 to give the actual IRFs for the corresponding exciting forces and RAOs cf equation 13 2 For practical purposes the JRn files will be most useful and the Rn files may be useful only to clarify the identity of the different columns in the JRn files Some experience and or trial computations will be needed to determine appropriate val ues of the input frequencies and time steps The dimensions of these parameters correspond to GRAV in the WAMIT run 13 5 OPTIONS 5 AND 6 The F2T utility has been developed primarily for use with Options 1 to 4 global forces and RAO s Local pressures velocities and wave elevations may be difficult to transform accurately due to limited or non convergence of the Fourier transforms at high frequencies The outputs from F2T include transforms of the WAMIT outputs fo
9. 700000 750000 800000 850000 900000 950000 000000 250000 500000 0 test17 cfg test17 pot Ker OO oO OC OD O 150000 400000 610000 660000 710000 760000 810000 860000 910000 960000 050000 300000 use default spl parameters input wavenumber output wavenumber FPrROOOOCOOOCOO Oo IRAD IDIFF 200000 450000 620000 670000 720000 770000 820000 870000 920000 970000 100000 350000 HH OoOoOOoOOOoOOoOOoOooOoO oO 250000 500000 630000 680000 730000 780000 830000 880000 930000 980000 150000 400000 eere OO Oo OO Oo Oo Oo Oo 300000 550000 640000 690000 740000 790000 840000 890000 940000 990000 200000 450000 NBETA array BETA follows NBODY XBODY IMODE 1 6 Input file testi7 gdf TEST17 cylinder with moonpool 1 9 80665 ULEN GRAV 1 1 ISX ISY 3 f NPATCH IGDEF 1 NLINES 0 5 1 0 0 25 radius draft moonpool radius Input file test17 frc TEST17 FRC Cylinder with moonpool 1 1 1 0 1 0 00 IOPTN 1 9 0 000000 VCG 0 500000 0000000 0000000 0000000 0 500000 0000000 0000000 0000000 0 500000 XPRDCT 0 NBETAH 1 NFIELD 0 0 0 0 0 0 Input file testi7a cfg TEST17A CFG file cylinder with moonpool free lid ipltdat 5 ilowgdf 5 ILOWHI 1 IALTFRC 2 ISOLVE 1 PANEL SIZE 0 2 use default spl parameters IPERIN 3 input wavenumber
10. ILOG is an integer parameter specifying the option to integrate the logarithmic singularity in the Green function separately with a more accurate numerical integration scheme ILOG 0 The logarithmic singularity is included with the wavelike component of the Green function and is integrated by quadrature over each panel ILOG 1 The logarithmic singularity in the Green function is subtracted and integrated analytically for pairs of panels for which the Rankine image singularity 1 r is also inte grated analytically This option produces more accurate results The default value is ILOG 0 ILOG 1 is required when panels are defined in the plane of the free surface including the following two cases 1 bodies with horizontal physical surfaces lying in the plane of the free surface and 2 use of the irregular frequency option where panels are located on the interior free surface inside the body waterline In these two cases execution of the program is interrupted with an error message if ILOG 0 ILOWGDEF is an integer parameter specifying the option to generate a low order GDF output file based on the input geometry see Section 5 7 If ILOWHI 0 the original input panels are used If ILOWHI 1 the low order output panels are generated from the panels of the higher order geometry If ILOWGDF gt 1 the panels are subdivided into ILOWGDFxILOWGDF sub panels ILOWGDF 0 Do not generate the output file gdf LOW GDF ILOWGDF gt 1 Generate
11. 1 HH ooo HOO OO OO O ONN oun 0 Orere Oooo test23 frc 1 0 0 0 IOPTN 1 9 RHO fluid density XCG IMASS IDAMP ISTIF NBETAH NFIELD no individual field points NFIELD_ARRAYS number of arrays Array is in exterior fluid domain NFX X1 DELX NFY Y1 DELY NFZ Z1 DELZ A 24 MOTIONS OF A HINGED VESSEL TEST24 The subroutine CCYLHSP IGDEF 32 is used to generate a horizontal circular cylinder with spheroidal ends as shown below The dimensions are specified in TEST24 GDF Two planes of symmetry are specified The cylinder is subdivided into five segments to permit the analysis of a vessel with transverse hinges between the segments Half of the middle segment and two others are in the domain x gt 0 Four patches are required for these three elements plus the spheroidal end The total number of segments specified in TEST24 GDF is used to read the x coordinates of the boundaries between adjacent segments and also the end of the vessel The total number of segments is equal to seven including five cylinders plus two spheroids Only the boundaries with coordinates x gt 0 are included in the last line of the GDF file since ISX 1 The generalized modes which represent the deflection of the hinges are defined in the subroutine HINGE MODES in the DLL file NEWMODES F designated by the parameter IGENMDS 22 in TEST24 CFG This subroutine reads the appropriate input data fro
12. The flow is assumed to be ideal and time harmonic The free surface condition is lin earized except in Version 6 45 where the second order free surface condition and body boundary conditions are imposed We refer to this as the linear or first order analysis Mean second order forces are included in this analysis since they can be computed rig orously from the linear solution The radiation and diffraction velocity potentials on the body wetted surface are determined from the solution of an integral equation obtained by using Green s theorem with the free surface source potential as the Green function The first versions of WAMIT up to and including Version 5 were based entirely on the low order panel method There the geometric form of the submerged body surface is defined by flat quadrilateral elements low order panels and the solutions for the veloc ity potential and or source strength are assumed constant on each panel Starting with Version 6 WAMIT was extended to include as an alternative option a higher order panel method based on a continuous B spline representation for the velocity potential and sev eral alternative schemes for defining the geometry of the body surface The order of the B splines is controlled by user specified input parameters The two different uses of the word order should be noted to avoid confusion Following 1 3 the usual conventions of marine hydrodynamics first order and second order are
13. When the low order method is used there are two different solutions which can be used referred to as the potential source formulations The potential formulation which is always evaluated represents the velocity potential in terms of surface distributions of sources and normal dipoles See Section 15 2 This is used to evaluate hydrodynamic quantities including the first order pressure force coefficients and drift forces based on momentum conservation Option 8 For the evaluation of these outputs the potential formulation is more general and efficient The source formulation is optional depending on the configuration parameter ISOR See Section 4 7 In the source formulation the potential is represented by a surface distribution of sources only as explained in Section 15 3 The source formulation must be used if the mean drift force and moment are evaluated by pressure integration also in some cases where the drift forces are evaluated using control surfaces Chapter 11 and more generally if the fluid velocity is required on the body surface The procedure for including the source formulation is used is described in Section 6 2 If the body has thin elements there are two possible approaches The first is to panel 6 1 both sides of these elements with a finite thickness to separate the two sides The disad vantage of this approach is that as a general rule the size of the panels must be comparable to the thickness and thus a ver
14. 0 27m as shown in the lower figure below The vertical elevation is required in this case since the gdf file only extends up to the original waterplane and trimming in roll or pitch about the center without vertical displacement would submerge half of the waterline with a gap above it Input file fnames wam test01 pot test01 frc test01 cfg Input file test01 cfg TESTO1 CFG cylinder R 1 T 0 5 ILOWHI 0 IRR 0 ipltdat 5 ISOR 1 omit ISOR in POT file include source formulation ISOLVE 0 use iterative solver ISCATT 0 solve for total diffraction potential not scattering ILOG 1 omit ILOG in POT file integrate log singularity IRR 0 omit IRR in POT file no irregular frequency removal MONITR 0 do not write FORCE output data to monitor NUMHDR 1 write headers to numeric output files Input file test01 pot TESTO1 POT cylinder R 1 T 0 5 ILOWHI 0 IRR 0 af HBOT 1 1 IRAD IDIFF 3 NPER array PER follows 8 971402 2 006403 1 003033 PER 1 NBETA array BETA follows O BETA 1 NBODY test01 gdf 0 0 0 0 HBOT XBODY 1 4 1 1 14 1 1 1 IMODE 1 6 First 10 lines of input file test01 gdf TESTO1 GDF circular cylinder R 1 T 0 5 ILOWHI 0 1 000000 9 806650 ULEN GRAV 1 1 ISX ISY 256 NEQN 0 0000000E 00 0 0000000E 00 0 5000000 0 0000000E 00 0 0000000E 00 0 5000000 0 1243981 1 2252143E 02 0 5000000 0 1250000 0 0000000E 00 0 5000000 0 1250000 0 0000000E 00 0 5000000 0 1243981 1 2252143E 02 0 5000
15. 0 are assigned in the FRC file This provides the necessary added mass damping exciting force and hydrostatic coefficients for use in modifying the RAO s A normal RAO numeric output file is also generated to serve as a guide for the format and contents of the external RAO file At this stage the user can prepare the external RAO file which must be named frc rao and correspond to the contents of the WAMIT output file frc 4 with the same definitions of the data cf Section 5 2 If IREADRAO 2 or 3 and IPOTEN 0 are assigned in the CFG file the program skips the POTEN computations and reads the solution from a previous run saved in the intermediate binary file pot p2f the filename pot of the POT input file must be retained for this purpose Then the program reads the RAO s from the external file frc rao and evaluates the hydrodynamic outputs for Options 5 9 using these values of the RAO s The two alternatives IREADRAO 2 and IREADRAO 3 are used to read the RAO s from the real and imaginary components columns 6 and 7 or modulus and phase columns 4 and 5 respectively If IREADRAO 2 there must be four real decimal numbers which correspond to the modulus phase real and imaginary components of each RAO as shown in Section 5 2 for OPTN 4 Arbitrary real numbers can be assigned to the modulus and phase since these are ignored If IREADRAO 3 only the modulus absolute value and phase in degrees are read and it is not necessary to in
16. 2 NBODY test05c gdf 0 0 1 25 0 0 0 0 Too ao A u a test05s gdf 0 0 0 5 0 0 0 0 1 1 1 1 1 Input file test05a frc TEST05a FRC array of field points 1 1 1i 1 0O 3 1 1 1 IOPTN 1 9 1 0 RHO fluid density test05c frc frc file for body 1 test05s frc frc file for body 2 0 NBETAH NFIELD no individual field points NFIELD_ARRAYS number of arrays Array is in exterior fluid domain NFX X1 DELX NFY Y1 DELY NFZ Z1 DELZ 0 1 0 1 Be l Re H O Ore N o qa Ooo o qa A 6 THE ISSC TENSION LEG PLATFORM TEST06 The added mass damping coefficients exciting forces motions and wave loads are evalu ated for the ISSC Tension Leg Platform in a finite water depth of 450 meters for three wave periods and one wave heading The TLP consists of four circular cylindrical columns and four rectangular pontoons as shown in the plots of the panel discretization The radius of each column is 8 435 meters The width and height of each pontoon are 7 5 meters and 10 5 meters respectively The distance between the centers of adjacent columns is 86 25 meters Further information is given by Eatock Taylor and Jefferys 7 Two planes of symmetry are used with 128 panels in one quadrant Thus there are a total of 512 panels on the complete surface The origin of the coordinate system is located at the intersection of the undisturbed free surface and the two planes of symmetry The characteristic length is set equa
17. However in TEST05 also in TEST13 the spheroid is rotated 90 about the vertical axis and this prevents the use of global symmetry In the modified Test05a the two bodies have the same relative orientations since the cylinder is axisymmetric but their centers are on the global y axis to avoid rotation of the spheroid about its vertical axis Thus in TEST05a the global symmetry indices are 1 0 and computational times are reduced substantially When NBODY gt 1 both the global symmetry and body symmetry for each body are output in the OUT file 8 9 8 6 OUTPUT The nondimensionalizations given in Chapter 3 hold for all output quantities L ULEN 1 the dimensional length for Body 1 is the characteristic length and is used for the nondi mensionalization of the output quantities The added mass A damping coefficients B and hydrostatic coefficients C i j are matrices of dimension up to 6N x 6N These quantities are defined in the direction of the axes of the corresponding body coordinate systems For example A is the added mass in the direction of the x axis of the coordinate system of Body 1 surge added mass due to the motion of the Body 2 in the direction of the z axis of Body 2 heave motion The forces X and the motion amplitudes are vectors of dimension up to 6N These quantities are also defined in the direction of the axes of the coordinates system of the corresponding body For example Xj7 is the pitch e
18. NN lt 99 IOUTFNAME 3 Append NNN to the filename 1 lt NNN lt 999 IOUTFNAME 4 Append _NNNN to the filename 1 lt NNNN lt 9999 The default value is IOUTFNAME 0 IOUTLOG is an integer parameter specifying the option to save a copy of the log file wamitlog txt with the filename of the output files see Section 5 9 IOUTLOG 1 Save a copy of the log file with the filename of the output files The default value is IOUTLOG 0 IPERIN is an integer parameter specifying the input data for PER in the POT file see Section 4 2 IPERIN 1 Input periods in seconds IPERIN 2 Input radian frequencies IPERIN 3 Input infinite depth wavenumbers IPERIN 4 Input finite depth wavenumbers The default value is IPERIN 1 The use of IPERIN is identical to the parameter IPERIO in Version 6 The name of this parameter is changed in Version 7 to correspond with the parameter IPEROUT IPEROUT is an integer parameter specifying the output data for PER The same four optional values IPEROUT 1 2 3 4 are used as defined above for the corresponding input parameter IPERIN The default value is IPEROUT 1 IPEROUT controls the first column of data in the numeric output files and also the first column of data in the header 4 28 of the OUT file showing the runtimes and iterations for the POTEN run as well as the same runtime outputs to the monitor during the POTEN run IPLTDAT is an integer parameter specifying the option to genera
19. Pds 15 53 Sb In equations 15 52 and 15 53 the integrations are over the exact body wetted surface Sb After substituting 15 48 15 50 and 15 51 and integrating the hydrostatic compo nents 3 1 FO zog 2 amp ary aa Jdl 1 oo o Jf 5i SVO Vot Era xZ Vojde ax a nods FO 15 54 63 aiy asx dl 1 E M Spg f x WIC XE ary anal ii bm fo RUA Po cn pax ff Ex 7ds ds p J Tods e 15 55 amp ayy Qz dl 15 12 where the hydrostatic components are FY pg wp arasy A203Y Ff a T 03 Zo k 15 56 af 105 Aupys Zo E23 Aup E301 AwpZo a203 L11 Loe 20103L15 Q1Q2VTp ilai a2 Vy i E1a2Awpr 6101 303 Aupys 504 305 Aupt Zo aA2AwpyfZo 1 3 Awp 302AwpZo a103 L11 Lo2 20303L12 102 022 it 15 57 Here is the first order runup Awp is the waterplane area and V is the volume of the body In addition x y are the coordinates of the center of flotation xp yp 2 are the coordinates of the center of buoyancy i 5 k are positive unit vectors relative to the x y z coordinates and Li Jp Livjds denotes the moments of the waterplane area 15 13 15 9 MEAN DRIFT FORCES USING CONTROL SURFACES The mean drift force and moment are evaluated by one the following two alternatives depending on the value of IALTCSF in the CFG file IALTCS
20. Since there is no diffraction potential to consider the velocity potential q in each tank is b iw gt gt Eb 15 62 and the first order pressure at a fixed point on the tank surface is given by P pg z S Zr amp 3 ay AX pOr 15 63 Here Zr is the vertical coordinate of the tank free surface above the origin The solution for the velocity potential q in each tank is computed simultaneously with the potential in the exterior fluid domain outside the hull using one extended linear system which includes all of the fluid domains exterior plus interior of all tanks The principal modification is to impose the condition that there is no influence between the separate fluid domains Thus the elements in the extended influence coefficient matrix are set equal to zero if the row and column correspond to different domains Further details are given in Reference 27 The force and moment exerted by the tank fluid on the vessel are given by F PNds P n axn ds 15 64 15 15 M P XxN ds ff P amp E axx x n a x n ds 15 65 where n is the normal pointing out of the tank away from the fluid domain of the tank and double integrals are over the submerged surface of the tank After some vector analysis these equations give relations similar to 15 52 15 53 for the contributions from the hydrostatic pressure Cr 3 3 pg f f nads Sr Cr 3 4 pg ynads Sr Cr 3 5 pg ff ongas ST Cr 4 4
21. The panel subdivision knot vector and the order of the B splines can be assigned independently between the geometry and the potential If the subdivisions and orders are the same this is analogous to the isoparametric approach in finite element analysis The domain of the parameters of the B splines representing the geometry is not limited to 1 1 Arbitrary limits can be used and they are normalized to 1 1 in the program More specifically the mapping function X X Y Z defined by Equation 7 3 is represented on each patch in the tensor product form M MP X u v 5 5 XyVi w Vj v 7 6 j l i l Here U u and Vi v are the B spline basis functions of u and v and M 9 and M are the number of basis functions in u and v respectively The superscripts are used to dis tinguish these geometric parameters from the corresponding parameters used to represent the potential in Section 7 2 As in 7 5 M9 NV KO 1 MONO KO 1 7 7 where K 9 and K are the orders of the respective B splines These parameters and the values of the unknown coefficients X are assigned for each patch in the GDF file The format of the GDF file is as follows header ULEN GRAV ISX ISY NPATCH 1 NUG 1 NVG 1 KUG 1 KVG 1 VKNTUG 1 1 VKNTUG NUA 1 1 VKNTVG 1 1 VKNTVG NVA 1 1 XCOEF 1 1 XCOEF 2 1 XCOEF 3 1 XCOEF 1 2 XCOEF 2 2 XCOEF 3 2 XCOEF 1 NB 1 XCOEF 2 NB 1 XCOEF 3 NB 1 7 9 NUG NPAT
22. WAMIT Version 6 this Option was designated as Option 9c When NBODY gt 1 a control surface surrounding each body is required and the drift force acting on each body is evaluated separately as in Option 9 The advantages of using the control surface are i all six components of the mean drift force and moment on a single body or on each one of multiple bodies are evaluated as in the pressure integration method and ii the computational results are more accurate than the pressure integration method when the body surface is not smooth especially for bodies with sharp corners The disadvantages are i the user must specify the control surface as an additional input and ii the evaluation of the momentum flux at a sufficiently large number of field points on the control surfaces increases the run time of the FORCE module This option is recommended when the accuracy of the mean forces and moments evaluated by pressure integration is uncertain due to slow or lack of convergence with respect to the discretization of the body The drift force and moment using a control surface are evaluated by one of two alterna tive methods These two alternatives are analytically equivalent In Alternative 1 based on equations 15 57 and 15 58 the contribution from the integral on the waterline WL is transferred to the line integral along the intersection of the free surface and the control surface CL Alternative 1 is generally more accurate for the horizo
23. When making a surface in MultiSurf the normal orientation is determined by 1 the orientations of parent entities 2 the order in which the parents are used and 3 the value of the orientation flag C 6 The orientation flag is handy because if a surface comes out with its normal opposite to what you want you don t have to rebuild the surface another way you just have to flip its orientation switch In MultiSurf we visualize the normal orientation by drawing an arrow at the parametric center of the surface u 0 5 v 0 5 in the positive normal direction This arrow is drawn whenever a surface is selected To see normal arrows simultaneously on all wetted surfaces you first need to have an option turned on this is under Tools Options on the General tab Auto Orientation needs to be All selected objects Then select all the wetted surfaces for example select the Entity List then Sdect Expand Entity Lists First Generation The orientation of non wetted construction surfaces doesn t matter as these are not included in the surface definitions accessed by WA MIT It is generally easier to see normals that point out of the geometry than those pointing inward For this reason our convention when making pane models for low order WAMIT and B spline surface models for HIPAN and high order WAMIT has always been to require outward normals on all wetted surfaces and then to reverse all normals automatically in the
24. entity name float index value entity name is the name of an entity in the model that has one or more floating point numbers in its properties For example a Point has 3 floats its X Y and Z coordinates or offsets a Bead has just one its t parameter or offset float index is an integer from 1 to the number of floats the entity has eg 1 to 3 fora Point 1 to 1 for a Bead value is the floating point value to substitute NPATCH Ooption Starting with WAMIT version 6 4 NPATCH can be specified as Oin an IGDEF 2 short form GDF This means figure out the number of patches from the Entity List or found on Line 7 This option is highly recommended because it avoids the need to count surfaces and the potential error of leaving surfaces out by specifying the wrong number for NPATCH N ote re symmetry The actual number of patches produced internally in WAMIT by this GDF is number of wetted surfaces x ISX 1 x ISY 1 x N where N is the number of rotational symmetry images The interface code does not need to count the X and Y symmetry images in indexing the patches All mirror image and XBODY transformations and mirror image indexing are performed inside WAMIT However NPATCH does need to count implicit rotational images produced by Z axis rotational symmetry N ote re Fortran READS Fortran will read this GDF with 5 LINES READ statements each reading a complete record This means any of the records except lin
25. follows 1 Color 11 bright cyan is reserved for dipole patches 2 Color 15 bright white is reserved for exterior free surface patches used for FDF file for the second order option 3 Color 4 red is reserved for free surface pressure patches Conventional patches body patches and interior free surface patches can be any other color besides 4 11 and 15 Surface colors are selected in the Properties M anager The Color Property dialog has a control allowing colors to be specified by color number 0 255 4 16 Internal tanks Internal tanks with liquid contents and a free surface can be represented in a model for WAMIT analysis see section 10 7 of the WAMIT User Manual In MultiSurf the tanks are modeled with surfaces and are communicated to WAMIT through a specially composed Entity List called the Tank list The name of the tank list is included in the short form GDF file as a second token on line 7 following the wetted surface entity list The tank list will have one entity for each internal tank this must be either 1 a surface entity when a single surface is enough to define the tank or 2 an entity list of surfaces for the tank in the usual case where multiple surfaces are required to define the tank It is possible to analyze the tanks alone without the enclosing body Just insert an empty Entity List say its name is empty in your model and use it for the wetted surface Entity List on line 7 o
26. free surface patches and no other entities An Entity List in general can legally contain entities of any type Check the contents of the Entity List and see that they are correct in number and identity Wetted surface Entity List includes a Trimmed Surface Trimmed surfaces are not eligible for usein WAMIT models for higher order analysis because they do not provide a complete square parameter space for distribution of the unknown potential You may be able to replace a Trimmed Surface with one or more SubSurfaces Surface entity is in error The RGKernel error code will be given This error code is compatible with the MultiSurf error system so it can be looked up in the MultiSurf reference manual or help system under Error codes The same error should occur when the model is opened in MultiSurf however this will not always be true because of the presence of incompatibilities between the two RGKernd dll versions See also remarks for error 6 12 The specified tank list was not found in the model A tank list was specified by name on line 7 of the GDF file but no entity with this name was found in the model First confirm that you are trying to perform analysis with internal tanks in this run if not line 7 should have only a single token the wetted surface Entity List name or Check that the second token on line 7 is the correct name for the tank list Entity names are case sensitive Check that an Entity List of this
27. not need to be running when the model is constructed in MultiSurf Communication between MultiSurf and WAMIT is solely through the M S2 model file created in MultiSurf and accessed by RG2WAMIT DLL 4 MultiSurf modeling considerations 4 1 Trimmed surfaces are excluded Trimmed surfaces TrimSurf and TrimSurf2 entities can only be handled for low order analysis ILOWHI 0 by the RG2WA MIT facility This is because WA MIT needs a complete parametric square over which to distribute its tensor product description of the unknown potential while a trimmed surface is by definition an arbitrary bounded portion of a parametric surface When ILOWHI 1 RG2WAMIT checks for the presence C 4 of Trimmed Surfaces in the wetted surface Entity List and returns an error when oneis encountered SubSurfaces on the other hand are perfectly legal for RG2WAMIT because they have like all other RG surface types except Trimmed Surface 4 sided topology and a full 0 1 x 0 1 parameter space One or more SubSurfaces can always cover a complex shaped region of a base surface where a single Trimmed Surface might otherwise be used 4 2 Optional wetted surface Entity List In order to be read and utilized through the WAMIT RGKernel interface an M S2 file model file may include an Entity List naming the wetted surfaces When this option is used WAMIT needs to be given the name of this Entity List in the GDF file see below Note In MultiSurf 5 a
28. 0 0 6 35602E 09 A 17 CYLINDER WITH MOONPOOL TEST17 This test run illustrates three alternative methods for analyzing bodies with moonpools The geometry used is the circular cylinder with a concentric fluid chamber as shown in the figure The inner chamber of fluid referred to as a moonpool is open at the bottom of the cylinder to the external fluid domain The top of the moonpool is a free surface with atmospheric pressure One of the practical aspects of this problem is the existence of highly tuned resonant frequencies of the motion at the moonpool free surface If the draft is comparable or large compared to the horizontal dimensions of the moonpool the principal resonance is a pumping mode which occurs when Kd the product of the wavenumber K and draft d is slightly less than one Additional resonances occur in sloshing modes at higher frequencies corresponding approximately to standing waves inside the moonpool A cylinder with draft 1m is used with the outer radius 0 5m and the inner radius 0 25m The geometry is represented analytically by the subroutine CYLMP IGDEF 7 In TEST17 three patches are used to represent the outer side r RADIUS the annular bottom z DRAFT and the inner side r RADMP The free surface inside the moonpool is part of the physical free surface and the appropriate free surface boundary condition is satisfied by the Green function as described in Chapter 15 The side of one quadrant is o
29. 0 950000 0 960000 0 970000 0 980000 0 990000 1 000000 1 050000 1 100000 1 150000 1 200000 1 250000 1 300000 1 350000 1 400000 1 450000 1 500000 1 NBETA array BETA follows 180 1 NBODY testi7a gdf 0 0 0 0 XBODY 10 1 0 1 0 IMODE 1 6 Input file testifc frc TEST17c FRC cylinder with surface pressure in moonpool fixed mode 7 1 1 1 0 0 0 00 IOPTN 1 9 7 1 1 1 1 1 1 0 0 000000 VCG 0 500000 0000000 0000000 0000000 0 500000 0000000 0000000 0000000 0 500000 XPRDCT 0 NBETAH 0 NFIELD A 18 ELASTIC COLUMN TEST18 The same inputs are used as in the low order test run TESTOS except for the GDF file The circular column is represented by the subroutine CIRCCYL IGDEF 1 Since the cylinder is bottom mounted NPATCH 1 and the patch on the bottom of the cylinder is omitted The draft is set equal to the fluid depth IGENMDS 18 is assigned in CFG file and in NEWMODES this results in a call to subroutine JACOBI for the four shifted Jacobi polynomials as described in Section 9 3 Input file test18 cfg TEST18 CFG bending of vertical column with 4 generalized modes ipltdat 5 ilowgdf 5 ISOLVE 1 NUMHDR 1 NUMNAM 0 NEWMDS 4 ILOWHI 1 IALTFRC 2 KSPLIN 3 IQUADO 3 IQUADI 4 IGENMDS 18 Input file test18 pot TEST18 POT bending of vertical column at resonance 200m depth 200 0 HBOT o 0 IRAD IDIFF 1 6 5 1 0 0 1 NBODY test18 gdf 0 0 0 0 0 0 0 0 o 0 0 O O 90 Input file
30. 13 59 49 err 0 There were EVAL calls RGKI DONE ri Executing RGK at 25 Nov 2001 13 59 49 8 Synopsis of operation The user generally will not need to know more about the functioning of the RG2WAMIT interface than has been explained in the operating instructions above However alittle more perspective may be useful in case error conditions are encountered or suspected The sequence of commu 1 During WAMIT s ini nication between the programs is as follows tialization process it opens and writes to an ASCII text file named RGKINIT TXT This file is located in the working folder It is created for each WAMIT run whether or not the run uses IGDEF 2 GDF s RGKINIT TXT contains for each body XBODY 1 4 plus the first 4 lines of any GDF in addition it contains the remainder of the GDF file whenever IGDEF 2 WAMIT calls the procedure RGKINIT in RG2WAMIT DLL This initializes the interface by using information read from RGKINIT TXT All specified mode files are opened and prepared for evaluation calls WAMIT makes as many calls as it needs to the procedure RGKEVAL in RG2WAMIT DLL Each such call evaluates one 3 D point at a specified u v parameter location o n one of the wetted surfaces furnished by the RG model 4 When finished with its RGKEVAL calls WAMIT makes one call to the procedure RGKDONE in RG2WAMIT DLL This frees all memory that was allocated during the RG
31. 2 EXSTIF 2 6 NEWMDS EXSTIF 6 NEWMDS 1 EXSTIF 6 NEWMDS 2 EXSTIF 6 NEWMDS 6 NEWMDS NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD The header IOPTN array and all lines beginning with the variable NBETAH are identical to the data in the Alternative form 1 FRC file The data which differ in Form 2 are described below RHO Dimensional density of the fluid in the same units as used for the external force matrices and for GRAV XCG YCG ZCG Dimensional coordinates of the body center of gravity in terms of the body coordinate system and in the same units as ULEN IMASS This index is either 0 or 1 to signify if the external mass matrix EXMASS is read If the value of the index is zero the matrix EXMASS is not included in the FRC file and the program assumes that all values in this matrix are zero If the value of the index is one the matrix EXMASS is included in the FRC file EXMASS is the 6 NEWMDS x 6 NEWMDS dimensional inertia matrix of the body about the body fixed axes For a conventional rigid body this is a 6 x 6 dimensional matrix as defined in Reference 3 page 149 equation 141 Each element in this matrix is added to the corresponding added mass of the body in setting up the equations of body motions IDAMP This index is either 0 or 1 to s
32. DOI C H Lee and J N Newman Boundary Element Methods in Offshore Structure Analysis OMAE 2001 Conference Rio de Janeiro 2001 Also published in Journal of Offshore Mechanics and Arctic Engineering Vol 124 pp 81 89 2002 DOI C H Lee and J N Newman Computation of wave effects using the panel method In Numerical Modeling in Fluid Structure Interaction Edited by S Chakrabarti WIT Press 2004 Link J N Newman Wave Effects on Vessels with Internal Tanks 20th International Workshop on Water Waves and Floating Bodies Spitsbergen Norway 2005 PDF C H Lee Evaluation of quadratic forces using control surfaces 2005 WAMIT Consortium Report 2005 PDF 29 J V Wehausen The motion of floating bodies Annual Review of Fluid Mechanics Vol 3 pp 237 268 1971 DOI 30 F T Korsmeyer H B Bingham and J N Newman A panel method program for transient wave body interactions PDI Appendix A DESCRIPTION OF TEST RUNS WAMIT V7 0 includes 37 standard test runs including 12 low order and 25 higher order applications These are designed to illustrate various different options and features of WAMIT and to help users to develop appropriate input files for their own purposes The following table gives relevant features of each test run In this table the first column tst denotes the name of the test run All of the corresponding input output files are assigned the filenames TESTtst Fo
33. FILE The optional Spline Control File SPL may be used to control various parameters in the higher order method These include the panel subdivision on each patch the orders of the B splines used to represent the potential and the orders of Gauss quadrature used for the inner and outer integrations over each panel If the SPL file is used it must have the same filename as the corresponding GDF file for the same body with the extension spl The format of the SPL file is as follows header NU 1 NV 1 7 KU 1 f KV 1 T IQUO 1 t IQVO 1 t IQUI 1 t IQVI 1 t NU 2 NV 2 7 KU 2 f KV 2 t IQUO 2 IQVO 2 t IQUI 2 IQVI 2 NU NPATCH NV NPATCH KU NPATCH KV NPATCH IQUO NPATCH IQVO NPATCH IQUI NPATCH f IQVI NPATCH NU and NV are the numbers of panels along the u and v coordinates KU and KV are the orders of B splines along the u and v coordinates These parameters should be greater than or equal to 2 Recommended values are given below IQUO and IQVO are the orders of Gauss quadrature for the outer integration These parameters should be greater than 1 and lt 16 Recommended values are given below IQUI and IQVI are the orders of Gauss quadrature for the inner integration These parameters should be greater than 1 and lt 16 Recommended values are given below NU NV marked by should not be specified in the SPL file when PANEL SIZE gt 0 is assigned in the configuration files See Section 4 7 In that ca
34. IRR 3 and ILOWHI 0 If IRR 3 is input using the low order method the program automatically generates a discretized interior free surface and stores the panel vertices in a special output file gdfidf In this file the vertices of the free surface panels are appended to the data in the GDF file Since this automatic discretization cannot accommodate abnormal waterline shapes the user should visualize the paneling on the interior free surface using the IDF file to check the quality of the interior free surface discretization When ISOR 0 the interior free surface is discretized with triangular panels based on the algorithm described in 8 The sides of the triangular panels are similar to the average length of the waterline segments An example is shown in the left figure of Figure 9 1 When ISOR 1 the interior free surface is discretized in a regular pattern of quadrilateral panels as shown in the right figure of Figure 9 1 Since the aspect ratio of the panels is O 1 the number of panels on the interior free surface is not so large as in the case ISOR 0 Connectivity between the free surface panels and the waterline segments is important in this case as explained in 16 The program first finds the centroid of the waterplane area enclosed by a waterline contour formed by a set of waterline segments Then the two nodes of each waterline segment are connected to the centroid forming triangles with vertices on the centroid and on the two nodes
35. If the wavemaker RAO s are normalized by these calculations of the wave elevations the results are directly comparable with the conventional RAO s in incident waves of unit amplitude When walls are specified by the parameters IWALLX0 1 and or IWALLY0 1 the program automatically reflects the body and wavemaker geometry about the walls The planes of symmetry for each body or wavemaker defined by the parameters ISX and ISY in the GDF file refer specifically to the local planes of symmetry of the body or wavemaker When IWALLX0 1 and wavemakers are defined in the wall X 0 the symmetry index ISX 0 should be used for the wavemakers similarly for wavemakers in the wall Y 0 ISY 0 Except for special cases where the GDF file only defines one half of the wavemaker both wavemaker symmetry indices should be zero The symmetry indices for bodies are the same as without walls Since the wavemakers correspond to one or more bodies it is necessary to include the usual inputs for these bodies in one or more FRC files However the dynamic characteristics of the wavemakers are ignored since the RAO s are not evaluated for the wavemakers Thus dummy values of the inputs for the dynamic characteristics of the wavemakers VCG and XPRDCT or XCT and external force matrics must be included but their values are not relevant 12 14 12 5 BODIES WITH PRESSURE SURFACES Starting in Version 7 0 it is possible to analyze problems where part of the body s
36. NEQN is always equal to the number of unknowns in the representation of the velocity potential on the body surface and interior free surface if IRR gt 1 The body surface is defined in the gdf file on NPAN panels in the low order method or NPATCH patches in the higher order method the gdf file also specifies the symmetry indices ISX ISY which define planes of symmetry x 0 y 0 respectively for the body as explained in Chapters 6 and 7 If one or two planes of symmetry are defined only one half or one quarter of the body surface is defined in the gdf file The program uses these symmetries to reduce NEQN when it is possible to do so by defining separate solutions which are symmetric and antisymmetric with respect to each plane of symmetry The number of the corresponding sets of influence functions or left hand sides is denoted by NLHS If there are no planes of symmetry NLHS 1 with one plane of symmetry NLHS 2 and with two planes of symmetry NLHS 4 Before considering possible modifications which may be required the value of NEQN is defined based on the inputs in the gdf file In the low order method NEQN NPAN is the number of panels on this surface In the higher order method Np NEQN 5 NU KU i 1 x NV i KV i 1 14 1 i 1 Here Np NPATCH is the number of patches NU and NV are the numbers of panels on each patch and KU and KV are the orders of the B splines used to represent the solution as explained in
37. NPATCH 6 with the patch indices 1 6 corresponding respectively to 1 the horizontal bottom 2 the vertical portion of the bow 3 sides of the mid body 4 ZAXIS 10 Sees A QS wh TS SESS TT TTT Ses ESSA HITS ett oesoses SSeS a a di SS ie ae ae ee es e oo E cere et P Coi OT ETAL KS ET A Mer a a a ZAXIS 30 a a As Sa Be i ee VOSS IN SST Wi eee NS TT Se SSE ATT TLL ASSES NEEM NSS a7 See Oy MEW SSE Re SST Figure 7 4 Perspective views of the torus with RCIRC 20 RAXIS 60 and three different values of ZAXIS as shown ZAXIS gt 0 in the top figure corresponds to the axis above the free surface In the middle figure the axis is in the plane of the free surface and the sections are semi circles In these two figures the torus is floating with the upper edges of the body in the plane of the free surface The bottom figure shows a complete submerged torus The dark lines indicate the boundaries between adjacent quadrants with one patch on each quadrant transom 5 sloping bottom on the prismatic stern and 6 sloping side on the prismatic stern The prismatic stern portion can be omitted by setting NPATCH 4 XAFT 0 0 HTRANSOM HBEAM and DTRANSOM DRAFT SPAR defines a spar with strakes and with an optional moonpool The number of patches varys depending on the optional configuration RADIUS is the radius of the spar DRAFT is the vertical length W
38. NY is the total number of cylinders in all four quadrants NX must be even no cylinders are in the plane X 0 NY may be odd or even If NY is odd the middle row of cylinders is centered on the X axis and only the upper half of each cylinder is represented There are two patches for each cylinder representing the side and bottom If INONUMAP 1 nonuniform mapping is used with finer discretization near the corners and waterlines ELLIPINT defines one side of an ellipsoid with internal tanks A B C are the semi axes of the ellipsoid ISX 0 and ISY 1 are used to permit the tanks to be assymmetrical about X 0 The tank vertices are defined by the array XVER as described above for FPSOINT If IRR 1 the internal free surface is represented by patch 2 GAPLID defines a rectangular lid in the free surface with one patch The lid extends from X X1 to X X2 and between Y GAP 2 and Y GAP 2 The entire surface of the lid is represented ISX ISY 0 Nonuniform discretization is used in the X direction if INONUMAP 1 in the Y direction if INONUMAP 2 and in both directions if INON UMAP 3 This subroutine can be used with appropriate generalized modes to establish an artifical damping lid on the free surface between two vessels CYLFIN defines the first 1 or 2 quadrants of a circular cylinder with symmetric fins in the plane x 0 RADIUS is the cylinder radius and WIDTH is the width of the fins Patch 1 is the side of the cylinder in quadrant 1 and patch 2 i
39. RAXIS ZAXIS 9 TLP 11 12 RADIUS DRAFT HSPACE WIDTH HEIGHT 10 SEMISUB XL Y1 Y2 Z1 22 DCOL RCOL NCOL 11 FPSO 4 6 XBOW XMID XAFT HBEAM HTRANSOM DRAFT DTRANSOM 12 SPAR RADIUS DRAFT WIDTH THICKNESS TWIST NSTRAKE IRRFRQ IMOONPOOL RADIUSMP IMPGEN 13 AUV 2 3 RADIUS DCYL DTAIL 14 SPAR 3 4 5 RAD1 RAD2 DRAFT SKIRT HEIGHT 15 SPHERXYZ 1 RADIUS X0 Y0 Z0 16 FPS02 7 10 XBOW XMID XAFT HBEAM HTRANSOM DRAFT DTRANSOM INONUMAP 17 FPSO12 7 10 XBOW XMID XAFT HBEAM HTRANSOM DRAFT DTRANSOM INONUMAP 18 TORUSELLIP 1 2 RCIRC RAXIS DRAFT 19 TORUS2 2 RCIRC1 RAXIS1 DRAFT1 RCIRC2 RAXIS2 DRAFT2 20 CIRCCYLH 2 3 RADIUS HALFLEN IGDEF 21 22 23 24 25 26 27 28 29 30 31 32 33 SUBROUTINE FPSOINT CIRCCYL ARRAY ELLIPINT GAPLID CYLFIN CYLFIN4 SKEW SPHERE CIRCOYL NOSYM ELLIPSOID NOSYM TANK BARGE INT BARGENUC CCYLHSP CIRCOYL MULTI NPATCH 23 4 4 6 9 Lo 1 2 3 12 13 GDF INPUTS XBOW XMID XAFT HBEAM HTRANSOM DRAFT DTRANSOM INONUMAP XBODY 3 XVER RADIUS DRAFT ASPACE NX NY INONUMAP A B C NTANKS XVER X1 X2 GAP INONUMAP RADIUS DRAFT WIDTH INONUMAP RADIUS DRAFT WIDTH INONUMAP RADIUS SKEW RADIUS DRAFT INONUMAP XS YS ZS A B C XS YS ZS XL XB XD SL SB SD HALFLEN HALFBEAM DRAFT HALFLEN HALFBEAM DRAFT STRIP NSEG RADIUS XSEG NCYL INONUMAP IBOT IFS RADIUS 1 DRAFT 1 XC 1 YC 1 RADIUS 2 DRAFT 2 XC 2 YC 2 RADIUS NCYL
40. Section 4 12 The optional Spline Control File gdf spl may be used in the higher order method as described in Section 7 11 The input file userid wam is read by both POTEN and FORCE to identify the licensee for output to the headers at run time and to write this information in the header of the out output file This file is prepared by WAMIT Inc and must be available for input to POTEN and FORCE at runtime To be available for input the file userid wam must either be copied to the default directory with other input output files or else the pathname indicating the resident directory must be listed in one of the configuration files as explained in Sections 2 1 and 4 7 Two alternative formats for the FRC files are described separately in Sections 4 3 4 For a rigid body which is freely floating and not subject to external constraints Alternative Form 1 Section 4 3 may be used with the inertia matrix of the body specified in terms of a 3 x 3 matrix of radii of gyration Alternative Form 2 Section 4 4 permits inputs of up to three 6 x 6 mass damping and stiffness matrices to allow for a more general body inertia matrix and for any linear combination of external forces and moments A third alternative format may be used for multiple bodies as described in Section 8 5 Several output files are created by WAMIT with assigned filenames The output from POTEN for use by FORCE is stored in the P2F file Poten to Force and automatically
41. Section 7 2 If the irregular frequency removal option is used with IRR 1 the interior free surface is included as a part of the surface defined in the gdf file and the value of NEQN defined above is unchanged But if automatic discretization of the interior free surface is utilized IRR gt 1 NEQN is increased by the program to include the additional unknowns on the interior free surface See Chapter 10 If waterline trimming is used ITRIMWL 1 the value of NEQN may change either increasing or decreasing depending on the trimming displacement and angles See Section 12 2 Reflection is performed automatically by the program if the planes of geometric sym metry x 0 and or y 0 of the body coordinate system do not coincide with the X 0 and or Y 0 planes of the global coordinate system This may occur in the following cases e if the input parameters XBODY 1 XBODY 2 or XBODY 4 which define the origin of the body coordinate system are nonzero in the POT file See Section 4 2 e for bodies near vertical walls Section 12 4 e for multiple bodies NBODY gt 1 as explained in Chapter 8 e If the trim angle about the x axis is nonzero symmetry about the plane y 0 is destroyed and vice versa In these cases the body surface is reflected NEQN is increased and NLHS is decreased When reflection about one plane of symmetry is required NEQN is increased by a factor of two and NLHS is reduced by a factor of one half When
42. Small gaps between them do not cause problems and they may even coincide without introducing numerical difficulties When irregular frequency removal is used IRR gt 0 the entire interior free surface inside the body should be described ignoring any possible intersections with tanks Thus the same interior free surface should be used with or without the presence of tanks Two types of tank parameters must be included in the CFG file as explained in Section 4 7 NPTANK is an integer array used to specify the panel or patch indices of internal tanks The data in this array are in pairs denoting the first and last index for each tank An even number of indices must be included on each line and each pair must be enclosed in parenthesis More than one line can be used for multiple tanks and or multiple tanks can be defined on the same line If NBODY gt 1 the body numbers for each body containing tanks must be appended to the parameter name Only integer data and parenthesis are read for the array NPTANK Other ASCII characters may be included on these lines and are ignored when the input data is read RHOTANK is a real array used to specify the density of fluid in internal tanks The density specified is relative to the density p of the fluid in the external domain outside the bodies as defined in Chapter 3 and Section 4 4 The data in the array RHOTANK must be input in the same order as the data in the array NPTANK Multiple lines of this para
43. TecPlot or other similar programs As in the case of the corresponding data files for visualizing the body surface the data in this file are defined with respect to the global coordinate system and when NBODY gt 1 there is only one output file with the filename associated to the first body When ILOWHICSF 1 and ILOWGDF gt 0 in the CFG file the file gdf_low csf is output This contains the data of the control surface in the low order form described in Section 11 2 TEST05 TEST13 and TEST22 show examples of using the control surface in the eval uation of the mean forces and moments 11 17 Chapter 12 SPECIAL EXTENSIONS 12 1 INTERNAL TANKS WAMIT includes options to analyze the linear hydrodynamic parameters for a fluid inside an oscillatory tank or to analyze the coupled problem where one or more tanks are placed within the interior of one or more bodies including their dynamic coupling Usually the fluid in each tank is bounded above by a free surface but in special cases a rigid boundary surface can be placed above the fluid to represent a tank entirely filled by fluid The following discussion pertains to the situation where a free surface is present in each tank The free surface boundary condition in each tank is linearized in the same manner as for the exterior free surface Special attention is required near the eigenfrequencies of the tanks where nonlinear effects are significant A two dimensional study of this problem includ
44. Ui u 0 f du p duf du J u is Jacobian and N denotes the number of pat as Following the Galerkin method 15 29 is multiplied by U and integrated over each patch This results in the linear system N 2rd bs gt gt Dik bs SP 15 30 k 1 for the radiation potential Similarly from 15 12 we obtain N Indi lon gt Dalen IF 15 31 k 1 for the diffraction potential In the above equations and Gp are unknown coefficients of basis function for the radiation and diffraction potentials respectively The matrices di and D and vectors SH and IF are defined by qi duyU uy U uy 15 32 H OG u uy D du U u i Auta Sy FC 15 33 SH duU u dun Cu uy J u 15 34 I ff duU peolu 15 35 As explained in Chapter 7 a set of B spline basis functions is defined by the order of the polynomial K and K and the number of panels N and N In general the basis function has nonzero value over a part of the patch For example U u Vm v is nonzero on the panels from l Ku 1 or 1 if l K 1 lt 1 to l th panels or Ny if L gt Nu in u and m K 1 or 1 if m K 1 lt 1 to mth or N if m gt N panels in v The integration in uy over each panel is referred to as the outer integration This is carried out by Gauss Legendre quadrature The order of the quadrature is specified by the input parameters IQUO and IQVO in the SPL file for u
45. XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD The first three lines of this file and all lines beginning with the variable NBETAH are identical to the data in the Alternative Form 2 FRC file FRC K is the name of the FRC file for body K The Form of each separate file must be 1 or 2 and this is specified by the optional array IALTFRCN in the configuration file as described in the following section Some of the data given in N FRC files are read but neglected if the same data is given in the GFRC file For example the data IOPTN and RHO in the FRC files for each body are neglected and the corresponding parameters provided by the GFRC file are used If fixed free modes are specified for multiple bodies using IALTFRC 3 the modifications described in Section 8 3 must be included only in the GFRC File and not in the FRC files 8 6 8 4 PARAMETERS IN THE CONFIGURATION FILES The configuration files described in Section 4 7 include several inputs that must be assigned separate values for each body These include IALTFRCN IGENMDS IRR NEWMDS NPFORCE NPNOFORCE NPTANK XBODY and XTRIM The procedure for doing this when NBODY gt 1 is to indicate the index of the corresponding body in parenthesis as shown below If IALTFRC 3 the array IALTFRCN must also be specified with values for each body unless the default values 1 are applicable for all bodies A typical configuration file used for all of the
46. always used here to refer to linearization of the boundary conditions and solution whereas low order and higher order refer to the method for representation of the body surface and solution The following quantities can be evaluated by WAMIT e Hydrostatic coefficients e Added mass and damping coefficients for all modes e Wave exciting forces and moments using the Haskind relations or directly by pressure integration from the solutions of the diffraction or scattering problems e Motion amplitudes and phases for a freely floating body e Forces restraining a body which is freely floating in some but not all modes e Hydrodynamic pressure and fluid velocity on the body surface e Hydrodynamic pressure and fluid velocity in the fluid domain e Free surface elevation e All components of the drift force and moment by momentum integration over a control surface e Horizontal drift forces and mean yaw moment by momentum integration in the far field e All components of the drift force and moment by local pressure integration over the body surface e Drift force and moment in bidirectional waves Two one or no planes of geometric symmetry may be present Part or all of the rigid body modes can be analyzed The program is designed to optimize the use of the available storage and minimize the computational effort for the specified planes of symmetry and modes Several techniques have been developed and implemented in WAMIT to improve t
47. analyses the motions of a vessel with five separate segments connected by hinges Further information is contained in the Appendix 9 1 INPUT FILES Two input parameters NEWMDS and IGENMDS control the implementation of the gener alized mode option NEWMDS specifies the number of generalized modes with the default value zero IGENMDS is an integer used to specify the definition of the generalized modes using either the DEFMOD program or the NEWMODES subroutine library IGENMDS is input in the configuration file The default value IGENMDS 0 is used if the program DEFMOD is used as explained in Section 9 2 If IGENMDS is nonzero the DLL file NEWMODES is used In the latter case the value of IGENMDS can be used to identify appropriate subroutines within the NEWMODES library as explained in Section 9 3 Different values of IGENMDS may be assigned for each body if NBODY gt 1 and the body numbers must be included as shown in Section 8 4 The definition of nondimensional outputs corresponding to each mode of motion cannot be specified in general without prescribing the dimensions of each mode To avoid this complication the parameter ULEN should be set equal to 1 0 in the GDF file whenever generalized modes are analyzed Except for this restriction the GDF and POT input files are not changed In the POT file the six rigid body modes can be specified as free or fixed in the usual manner by appropriate choices of the index IRAD and array MODE
48. and appropriate code for computing the vectors u vj wj DEFMOD should then be compiled and linked with an appropriate FORTRAN compiler Since DEFMOD is a self contained FORTRAN 9 5 file linking is a trivial operation DEFMOD is executed after the first run of WAMIT using the gdf PRE file as input to generate the output file gdf MOD This MOD file generated by DEFMOD includes the normal velocities of each generalized mode at each panel centroid Also included at the end of this file are the generalized hydrostatic coefficients computed from equation 9 12 After creating the gdf MOD input file execute WAMIT again to continue the run From this on to the completion of the run the procedure is identical to that where NEWMDS 0 The first and second runs are distinguished by the absence or presence respectively of the file gdf MOD Thus the existence of an old file with the same name is important If changes are made only in the POT file e g changing the wave periods an existing MOD file can be reused without repeating the first run of WAMIT On the other hand if changes are made in the GDF file e g changing the number of panels and if the same gdf filename is used for the new GDF file the old MOD file must be renamed or deleted before running WAMIT If changes are made in DEFMOD e g changing the definitions and or number of new modes the old PRE file can be used as input to create the new MOD file A warning message is iss
49. and are not present in the CSF file 11 15 Example 5 Monohull with one plane of symmetry as in TEST22 FPSO with internal tanks using a rectangular outer control surface 1 ILOWHICSF O 1 ISX ISY 0 0 2 NPATCSF ICDEF PSZCSF 1st two indicate this is automatic 1 NPART 4 nvo 12 0 0 0 12 0 3 0 12 0 3 0 12 0 0 0 In this case the outer rectangular boundary has four vertices starting on the x axis and ending on the x axis When automatic representation of the CSF is implemented the program traces the body waterline s and establishes extra patches or panels on the free surface between these waterlines and the partition boundaries When the program connects adjacent sides of patches in the waterline the patches or panels are identified based on the coincidence or close proximity of their vertices The parameter TOLGAPWL is used for this purpose to allow for small gaps or overlaps between adjacent patches at the waterline The default value TOLGAPWL 10 7 is used unless a different value of this parameter is defined in the CFG file as explained in Section 4 7 In the test for adjacent patches the nondimensional Cartesian coordinates of the adjacent patch corners are evaluated and the distance between these points is computed The patches are assumed to be connected if this distance is less than either TOLGAPWL or the product of TOLGAPWL and the maximum length of one of the patch sides The latter value is introduced to allo
50. are considered Dipole panels patches wavemakers and the waterlines of interior tanks are not included Field points on the free surface of interior tanks are not included in this test Users should verify the identification of interior field points especially in cases where the shape of the waterline is unusual or irregular 4 4 THE FORCE CONTROL FILE Alternative form 2 In this Section the second alternative form of the FRC file is described where it is possible to specify separately three independent external force matrices including the mass matrix of the body an external damping matrix and an external stiffness matrix This permits the analysis of bodies which are not freely floating in waves with arbitrary linear external forces and moments and also permits the specification of the complete body mass matrix instead of the simpler radii of gyration cf Section 4 3 The format of the Alternative 2 FRC file is shown below header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 RHO XCG YCG ZCG IMASS EXMASS 1 1 EXMASS 1 2 EXMASS 1 6 NEWMDS EXMASS 2 1 EXMASS 2 2 EXMASS 2 6 NEWMDS EXMASS 6 NEWMDS 1 EXMASS 6 NEWMDS 2 EXMASS 6 6 NEWMDS IDAMP EXDAMP 1 1 EXDAMP 1 2 EXDAMP 1 6 NEWMDS EXDAMP 2 1 EXDAMP 2 2 EXDAMP 2 6 NEWMDS EXDAMP 6 NEWMDS 1 EXDAMP 6 NEWMDS 2 EXDAMP 6 6 NEWMDS ISTIF EXSTIF 1 1 EXSTIF 1 2 EXSTIF 1 6 NEWMDS EXSTIF 2 1 EXSTIF 2
51. are included in Section 14 7 7 10 BODIES WITH THIN SUBMERGED ELEMENTS The higher order method can be used to analyze bodies which consist partially or com pletely of elements with zero thickness as in the analogous extension of the low order method described in Section 6 3 In the higher order method the patches representing these elements are referred to as dipole patches Dipole patches are represented in the same manner as the conventional body surface Since both sides of the dipole patches adjoin the fluid the direction of the normal vector is irrelevant On the dipole patches the unknowns are the difference of the velocity potential A positive difference is defined to act in the direction of the normal vector As an example the floating spar shown in Figure 6 2 is analyzed by the higher order method in Test Run 21 The total number of patches is seven three on the side of the cylinder three on the strakes and one on the bottom of the cylinder The indices of the patches on the side are 1 3 and 5 the strakes are 2 4 and 6 and the bottom is patch number 7 When dipole patches are used the mean drift force moment can be evaluated by the momentum method Option 8 and in some cases by the use of a control surface Option 7 as described in Chapter 11 The direct pressure method Option 9 cannot be used and a warning message is output when this option is specified A symmetry plane can be used when there are flat th
52. array PER follows 0 1 0 5 1 0 2 NBETA array BETA follows 0 0 45 end of file 1 NBODY test09 gdf 0 0 0 0 HBOT XBODY 1 4 1 141 14 1 1 1 IMODE 1 6 Input file test09a frc TESTO9A FRC Spar with three strakes trimmed waterline 1 1 1 1 1 3 0 2 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 23 0 0 15 15 0 5 end of file A 11 CIRCULAR CYLINDER TEST11 The same cylinder used for the low order TESTO1 is used here with the higher order option ILOWHI 1 Two alternatives are used for the geometry In TEST11 the geometry is defined by B splines IGDEF 1 The parameters knot vectors and coefficients for each patch are contained in the file TEST11 GDF It should be noted that the circular patches and boundaries cannot be fit exactly with B splines however the geometric errors are generally much smaller in this case compared to the flat panel representation in TESTO1 For example the maximum error of any point output in the data file test11 pnl is less than 3E 5 and the maximum error in the computed volume is 1E 5 By comparison using the flat panel discretization in TESTO1 the maximum error in the computed volume is 3E 3 Thus when the higher order method is used the principal errors in the results should be associated with the approximation of the potential by B splines as opposed to the representation of the geometry This a
53. as follows Option Description Filename 1 Added mass and damping coefficients fred 2 Exciting forces from Haskind relations fre 2 3 Exciting forces from diffraction potential fre 3 4 Motions of body response amplitude operator freA 5p Hydrodynamic pressure on body surface fre 5p 5v Fluid velocity vector on body surface fre 5vx 5vy 5vz 6p Pressure free surface elevation at field points fre 6p 6v Fluid velocity vector at field points fre 6vx 6vy 6vz 7 Mean drift force and moment from control surface _frc 7 8 Mean drift force and moment from momentum fre 8 9 Mean drift force and moment from pressure fre 9 The evaluation and output of the above parameters is in accordance with the following choice of the corresponding index IOPTN I 0 do not output parameters associated with Option I IOPTN I 1 do output parameters associated with Option I Options 2 9 may have additional values as listed below IOPTN 2 and IOPTN 3 IOPTN I 0 do not output the exciting forces IOPTN I 1 output the exciting forces IOPTN I 2 output the exciting forces and also the separate Froude Krylov and scattering components of these forces see Sections 3 3 and 5 3 IOPTN 4 IOPTN 4 0 do not output the response amplitude operator RAO IOPTN 4 1 output the RAO using the Haskind exciting force IOPTN 4 2 output the RAO using the diffraction exciting force IOPTN 4 3 output field data only for specified radiation mod
54. as follows e Explicit lines of input must be included for IRR n with n 1 2 N where N lt NBODY e If N lt NBODY the remaining elements for N lt n lt NBODY are assigned with the same value as IRR N For example if NBODY 3 the inputs IRR 1 1 and IRR 2 3 will result in IRR 3 3 whereas if IRR 1 1 is the only input then all three elements are assigned IRR 1 As signing only IRR 2 or IRR 3 will result in an error message and halt excution of the program Test13a illustrates this scheme in the case where the cylinder is trimmed and the spheroid is untrimmed The interior free surface of the spheroid is generated by the sub routine ELLIPSOID in GEOMXACT F Since the cylinder is trimmed it cannot use the standard definition of the interior free surface generated by the subroutine CIRCYL As shown in Appendix A 13 the GDF and SPL inputs for the spheroid are the same as one would used with IRR 1 whereas the inputs for the cylinder specify IRR 3 and do not include the interior free surface In this case the interior free surface of the cylinder is elliptical due to the trim angle and different values of NU are assigned on the deep and shallow sides due to the corresponding depths of the exterior patches Chapter 11 MEAN DRIFT FORCES USING CONTROL SURFACES If IOPTN 7 gt 0 in the FRC file the mean drift force and moment are evaluated from the control surface momentum flux method with output in the OPTN 7 or frc 7 file In
55. axis of the wall system as defined in Figure 12 1 The values of the incident wave heading angles BETA are defined with respect to the positive X axis An important detail to note is the definition of the incident wave amplitude and its physical interpretation The incident wave is defined as the incoming wave component 12 12 prior to reflection from the wall s and A is the corresponding amplitude If only one wall is present then after reflection the resulting wave field in the absence of the body is an oblique standing wave with maximum free surface elevation 2A In the special case 5 0 the incident wave propagates parallel to the wall without a distinct reflected component but the physical amplitude of this wave is 2A Some consequences of this definition are noted in the comparison of Test Runs 04 and 19 see Sections A 4 and A 19 If two walls are present the resulting wave motion after reflection from both walls will have a maximum elevation of 4A In the Force Control File the array IOPTN is unchanged from the definitions in Section 4 3 Since momentum integration cannot be used to determine the mean drift force and moment IOPTN 8 1 is ignored IOPTN 9 is used in the normal manner to evaluate the drift force and moment from pressure integration IOPTN 7 can be used provided the control surface is within the fluid domain The Haskind wave heading angles BETAH are defined with respect to the walls in the same manner as BET
56. between RGKernd dll versions this error might occur through no fault of the user AeroHydro should investigate Note a table is built for each surface in the model even when Accurate evaluation is specified Unexpected end of linein RGKINIT TXT A file record in RGKINIT TXT did not contain all required data For example if the file line giving fast accurate divisions multiplier and inward normal settings has only one or two tokens this error will occur Check that your GDF file contains all required information and that NLIN ES is correct Wetted surface Entity List has fewer than NPATCH surfaces The GDF file specifies NPATCH the number of surfaces to use in the solution for a given body the Entity List does not contain the full complement Check that NPATCH is correctly specified in the GDF Open the MS2 filein either M ultiSurf or Notepad and check that all wetted surfaces and or interior free surface patches are in the Entity List If the number of surfaces is large making counting difficult select the Entity List in MultiSurf often Select By Nameis the easiest way and the number of its parents will be indicated in the Properties M anager Visually you can select the Entity List and Select Expand Entity Listts First Generation all surfaces in the list will then be highlighted Wetted surface Entity List contains a non surface entity The wetted surface Entity List must contain all the wetted patches and or interior
57. body For example if there are three bodies and body 1 has 3 free beam bending modes defined by NEWMODES DLL body 2 has no generalized modes and body 3 has 2 moonpool free surface lids four lines should be added to the configuration file as follows NEWMDS 1 3 IGENMDS 1 16 NEWMDS 3 2 IGENMDS 3 17 It is not necessary to include the additional lines NEWMDS 2 0 and IGENMDS 2 0 since zero is assigned by default but these explicit inputs may be added for clarity In the approach described in Section 9 2 prior to the NBODY run of WAMIT the subroutine DEFMOD must be executed for each body to prepare the corresponding MOD file This procedure is carried out separately for each body for which generalized modes are specified with an appropriate subroutine DEFINE corresponding to the generalized modes of that body The procedure for doing this is identical to that described in Section 9 2 for a single body In the approach described in Section 9 3 the subroutines in NEWMODES should be organized in a logical manner so that the generalized modes for each body are defined Usually this can be done most effectively by using separate subroutines for each body but that is not necessary The body index IBI is used to identify the body for each call The numbering sequence for these modes in the output files is with the new modes of each body following the six rigid body modes of the same body Thus in the example above the nine exciting f
58. can be obtained more efficiently with the higher order method 2 Various forms of geometric input are possible including the explicit representation When it is possible to use this approach it is relatively simple to input the geometry and modify its dimensions for each run 3 The pressure and velocity on the body surface are continuous Continuity of the hydrodynamic pressure distribution is particularly useful for the analysis of structural loads 4 The higher order method usually gives a more accurate evaluation of the free surface elevation runup at the body waterline This is particularly important when the mean drift forces are evaluated using a control surface as described in Chapter 14 Disadvantages 1 The linear system which must be solved for the velocity potentials is not as well conditioned in the higher order method Thus the iterative method for the solution of the linear system fails to converge in many cases The direct or block iterative solution options are recommended in these cases Since the size of the linear system number of unknowns is significantly smaller than for the low order method this generally does not impose a substantial computational burden 2 The second order pressure due to the square of the fluid velocity is unbounded at sharp corners The approximation of this pressure by higher order basis functions is more difficult than in the low order method The result may be less accurate unless the
59. components are output separately the nondimensional velocity due to jth mode is defined by T V E V KL KLVo J vL Pi Here V v Vy is the dimensional fluid velocity and v iw denotes the velocity of the body for 7 1 2 3 and the angular velocity for 7 4 5 6 n 0 for j 1 2 3 and n 1 for j 4 5 6 Special definitions are required in the limits of zero and infinite wave periods as ex plained in Section 3 9 3 8 3 8 MEAN DRIFT FORCE AND MOMENT The definition of the nondimensional mean drift force and moment in unidirectional waves is E F F pgA L where k 1 for the forces i 1 2 3 and k 2 for the moments i 4 5 6 For bi directional waves of the same period with complex amplitudes A 45 and corresponding angles of incidence 61 62 the nondimensional outputs F 61 82 are the coefficients such that the total dimensional mean drift force or moment exerted on the body is given by the equation F B1 62 pgL 41 F 81 61 Aol Fi Bo B2 2Re A1 ASF Bo Note that F 62 81 F 1 82 where the asterisk x denotes the complex conjugate In Option 7 the drift force and moment are evaluated based on the momentum flux across a control surface as described in Chapter 11 using equations 15 57 60 In Option 8 the evaluation of the horizontal drift force and vertical moment is based on the momentum conservation principle in its general form see References 4
60. coordinate system If NBODY gt 1 the panels of all bodies are merged with a common index K following the same order as the body parameters in the POT file See Chapter 8 If IDIFF 1 is used to compute outputs for radiation modes as described in Section 4 3 forced motions in calm water the wave heading angle BETA 0 is shown in the numeric output files for options 5 9 5 3 FROUDE KRYLOV AND SCATTERING FORCES The separate Froude Krylov and scattering components of the exciting force and moment can be evaluated by setting the index IOPTN 2 2 and or IOPTN 3 2 in the FRC file as explained in Section 4 3 In this case additional numeric output files are generated by the program with the extensions 2fk and 2sc for the Haskind forces and 3fk and 3sc for the diffraction forces These files contain the Froude Krylov and scattering components respectively in the same format as shown above for the OPTN 2 and OPTN 3 files These 5 4 are defined in Section 3 3 The Froude Krylov outputs in the 2fk and 3fk files are identical 5 4 BODY PRESSURE FOR THE HIGHER ORDER METHOD If the higher order method is used ILOWHI 1 Option 5 is selected in the FRC file and IPNLBPT 0 the pressure and the fluid velocity on the body surface are output at the points corresponding to equally spaced points in parametric space These points are defined in parametric space as the midpoints of the set of KU 1 KV 1 panel subdivisions on each patch
61. corresponding data for the hull When the higher order option ILOWHI 1 is used the header of the out file includes a list of all the patches and the corresponding tank numbers ITANK for patches which are defined as interior tanks When ITRIMWL 0 or ZTANKFS is not included in the CFG file the values of ZTANKFS displayed in the header of the out file correspond to the tank free surface elevations as used in the program derived from the upper boundary of the tank surfaces Hydrodynamic parameters which are physically relevant for the tanks alone Options 1 5 6 9 can be computed by inputting only the patches or panels for the tanks In this case IDIFF 1 should be used and the outputs for options 5 6 9 correspond to the combination of radiation modes specified by the IMODE array with unit amplitude of each mode The damping coefficients for the tanks should be practically zero From momentum conservation the horizontal drift forces and vertical drift moment from Option 9 should be practically 12 4 Zero Internal tanks affect the hydrostatic restoring coefficients Cj as described in Section 15 10 The hydrostatic matrix which is output in the out and hst files includes the effects of the tanks For example the hydrostatic coefficient C33 in the output files is equal to the total area of the waterplane inside the waterline of the body minus the product of the free surface area and density for each tank When both tanks and the external h
62. defines a sphere of radius RADIUS with its center at X0 Y0 Z0 If RADIUS lt Z0 lt RADIUS the sphere is partially submerged and if ZO lt RADIUS it is completely submerged If XO 0 ISX 1 and vice versa If YO 0 ISY 1 and vice versa FPSO2 defines an FPSO with one extra patch on the bottom in the bow to provide a more uniform mapping of the bottom relative to the subroutine FPSO described above If NPATCH 10 the interior free surface is included for use with IRR 1 INONUMAP 0 gives a uniform mapping on all patches INONUMAP 1 gives a nonuniform mapping with finer discretization near the chines and INONUMAP 2 gives a nonuniform mapping with finer discretization near both the chines and waterline Uniform mapping is used for the prismatic stern in all cases FPSO12 defines NBODY 2 FPSO S with different dimensions This subroutine illus trates the use of one subroutine to define multiple bodies of the same type with different dimensions In all other respects it is the same as FPSO2 described above The same value of INONUMAP must be used for both bodies TORUS_ELLIP Torus with elliptical sections This subroutine is the same as TORUS described above except that the generating sections are elliptical with their centers in the free surface The horizontal semi axis of the ellipses is equal to RCIRC and the vertical semi axis is equal to DRAFT It is required that RAXIS gt RCIRC i e there is a free surface in the center of the toru
63. due to the combination of vertical trim and rotation see the equations in Section 12 2 The differences in the rigid body inertia coefficients are shown in the MMX files Input file test22a cfg TEST22a CFG fpso with 2 interior tanks trimmed waterline ipltdat 4 ILOWHI 1 ILOG 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 NPTANK 8 11 12 15 RHOTANK 1 0 1 0 relative densities of tank fluids ITANKFPT 1 tank field points are in frc file ztankFS 1 0 0 0 ITRIMWL 1 XTRIM 1 0 O 15 0 Input file test22a pot TEST22a POT fpso with 2 interior tanks trimmed waterline 1 0 1 1 IRAD IDIFF 3 2 0 2 5 3 0 1 NBETA array BETA follows 90 1 NBODY test22a gdf 0 0 0 0 XBODY 11 1 1 1 1 IMODE 1 6 Input file test22a gdf TEST22 GDF fpso with 2 tanks trimmed waterline 1 9 80665 ULEN GRAV O 1 ISX ISY 15 21 NPATCH IGDEF 36 NLINES 4 16 2 3 15 2 XBOW XMID XAFT 2 2 1 2 HBEAM HTRANSOM 2 2 1 6 DRAFT DTRANSOM 0 0 0 INONUMAP XBODY 3 2 000000 0 000000 1 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 0 000000 0 000000 0 000000 0 000000 0 000000 0 000000 0 000000 0 000000 0 0 NONNONODOONNNN 000000 000000 2 000000 2 000000 0 000000 2 000000 0 000000 0 000000 2 000000 2 000000 2 000000 2 000000 2 000000 Input file 100000 100000 000000 100000 1
64. following modified format OPTN 5P PER M K Re p Im p Re po Im p PER BETA M K Re pp Im pp Here denotes the remaining components for modes 3 4 5 6 if the six rigid body modes are 5 2 ke o specified for a single body More generally when different sets of modes are evaluated for one or multiple bodies these are output in sequence For each wave period the radiation pressures are listed for all values of M and K before the diffraction pressures Correspond ing formats apply for the fluid velocity components in the files OPTN 5vx OPTN 5vy OPTN 5vz If Option 5 is specified and IPNLBPT 0 the supplementary output file gdf PNL is created in the following format gafPNL M K XCT YCT ZCT AREA mns ny nz Xn rxn rxn If Option 6 is specified and INUMOPT6 1 the numeric output files 6p or 6vx 6vy and 6vz contain the separate components of the radiation and diffraction pressure and velocity in the following modified format OPTN 6p PER L Re p Im pi Re po Im po PER BETA L Re pp Im pp Here denotes the remaining components for modes 3 4 5 6 if the six rigid body modes are specified for a single body More generally when different sets of modes are evaluated for one or multiple bodies these are output in sequence For each wave period the radiation pres sures are listed for all values of L before the diffraction pressures Corresponding formats apply for the fluid velocity components in the files OPTN 6v
65. follows Parameter Default value IALTCSF 1 IALTFRC IBODYW ICCFSP IDELFILES IFIELD ARRAYS IFORCE IGENMDS ILOG ILOWGDF ILOWHI IMODESFSP INUMOPT5 INUMOPT 6 IOUTFNAME IOUTLOG IPERIN IPEROUT IPLTDAT IPNLBPT IPOTEN IQUADI IQUADOY IREADRAO IRR ISCATT ISOLVE ISOR ITANKFPT ITRIMWL SoS OS a SS OS j coooocooowrRroOrrcooc OO IWALLXO IWALLYO KSPLINt MAXITT MAXMIT MODLST MONITR NCPU NEWMDS NFIELD_LARGE NMODESFSP NOOUT NPDIPOLE NPFORCE NPFSP NPNOFORCE NPTANK NUMHDR 0 NUMNAM 0 PANEL_SIZE 1 0 RAMGBMAX 0 5 RHOTANK SCRATCH_PATH current directory TOLFPTWL 1 E 3 TOLGAPWL 1 E 3 USERID_PATH current directory VMAXOPT9 1 0 XTRIM ZTANKFS These parameters only need to be included when they are required Parameters where a specified default value is shown are assigned this value when the parameter is not included explicitly The parameters marked f are spline control parameters defined in Sections 7 11 12 These can be input either in the cfg or spl file oO Ww Or Ke OoOocr Oo O When multiple bodies are analyzed NBODY gt 1 there are additional parameters and some of the parameters in the list above must be assigned with separate values for each body See Section 8 4 Explanations of the parameters which may be specified in the configuration file are as follows IALTCSF is an integer specifying the alternative methods of evaluating the mean drift force and moment using a control surf
66. for modified versions of test07 ISSC TLP and test15 Semi Sub for values of NCPU between 1 and 8 The test07m inputs are the same as in Appendix A 7 except that the number of panels NPAN 4048 and the number of wave periods NPER 32 The testl m inputs are the same as in Appendix A 15 except that NPER 32 These computations were run on a Dell T7500 PC with 8 CPUs and 96 Gb of RAM under the Windows XP Pro x64 operating system The principal advantage of multiple processing is in the computing time for loops over the wave period During the run when the time and number of iterations are output for each wave period on the monitor these are displayed in groups of NCPU lines more or less simultaneously with values of the wave period which usually are not in a logical sequence The original sequence is restored in the header of the out output file where it will be noted that the clock time for each wave period is not sequential Testl4a is a useful example of this process and of the advantage of using multiple processors for runs with a large number of wave periods See Appendix A 14 When NCPU gt 1 the value of NCPU used is shown in the wamitlog txt output file If the total number of wave periods NPER is less than the value of NCPU in the configuration files NCPU is reduced for the loops over the wave period and the reduced value is displayed in the wamitlog txt file Maximum efficiency of the computing time is achieved when NPER is an integer
67. gdf TEST14 ISSC TLP ILOWHI 1 43 125 9 80665 ULEN GRAV 1 1 ISX ISY 12 9 NPATCH IGDEF 2 NLINES 8 435 35 43 125 RADIUS DRAFT HSPACE 7 5 10 5 WIDTH HEIGHT Input file testi4 spl TEST14 ISSC TLP ILOWHI 1 L lt 2 NU NV patch 1 E2 NU NV patch 2 1 2 NU NV patch 3 1 2 NU NV patch 4 1 2 NU NV patch 5 1 2 NU NV patch 6 1 2 NU NV patch 7 1 2 NU NV patch 8 4 1 NU NV patch 9 4 2 NU NV patch 10 4 1 NU NV patch 11 1 1 NU NV patch 12 Input file test14 frc TEST14 ISSC TLP ILOWHI 1 IALTFRC 2 1 1 1 2 0 0 0 1 1 IOPTN IOPTN 4 lt 0 signifies fixed modes 6 NDFR 110001 IMODE T RHO 0 0 3 0 XCG 1 IMASS 53066 4 O O O 159199 2 O 0 53066 4 Os 159199 2 O 0 0 O 53066 4 0 O O 0 159199 2 0 8 0201552E7 O O 159199 2 O O O 8 0201552E7 O O O 0 Oy O 9 54906731E7 0 IDAMP 0 ISTIFF 0 NBETAH 0 NFIELD Input file testi4da cfg ILOWHI 1 IRR 0 ISOLVE 1 IQUADI 4 IQUADO 3 KSPLIN 3 NUMHDR 1 IALTFRC 2 IPERIN 2 IPEROUT 2 Input file testi4a pot TEST14A ISSC TLP ILOWHI 1 450 0 0 IRAD IDIFF 101 NPER array PER follows 0 05 0 05 1 NBETA array BETA follows O 1 NBODY test14 gdf 0 0 0 0 XBODY 1 0 10 1 20 IMODE 1 6 Input file test14a frc TEST14A ISSC TLP ILOWHI 1 IALTFRC 2 1 1 1 1 0 0 0 0 O IOPTN 1 RHO 0 0 3 0 XCG 1 IMASS 53066 4 O 0 O 159199 2 0 O 53066 4 O 159199 2 O 0 O O 53066 4 0 O 0 O 159199 2 O 8 0201552E7 O 0 159199 2 O
68. higher order solution method This feature is availablein WAMIT versions 6 1 and higher RGKernd is the C library of mathematical geometric and data storage functions that supports M ultiSurf SurfaceWorks and other RG applications It is compiled asa DLL In this project a second DLL was developed to provide the interface between WAMIT s Fortran code and RGKernel s C procedures The advantages of this integration are 1 Accuracy RG geometry definitions are fundamentally exact and in practice can be evaluated to a high degree of precision This is in contrast to faceted and N URBS based geometric representations whose accuracy is commonly compromised by approximations Accuracy of surface surface junctions is critical in WAMIT s high order analysis method 2 Convenience When MultiSurf is used to develop WA MIT models for this interface the user avoids all further effort to develop panel files for the low order method or B spline approximation files as have been needed for the high order method The Geometric Data File GDF is usually 8 lines for each body defined by this method The purpose of this document is to provide instructions for use of this new WAMIT feature The topics include Supported features and options Required files versions and locations MultiSurf modeling considerations GDF file format Log file RGKLOG TXT Error conditions 1 1 New features for WAMIT version 6 4 New features introduced to the RG2
69. in Chapters 8 10 for the appropriate modifications of the input files for specific purposes including the analysis of multiple bodies generalized modes of body motion and the removal of irregular frequency effects The execution of a WAMIT run is divided between two subprograms POTEN and FORCE as explained in Chapter 1 In special circumstances it is useful to run WAMIT and execute only one of the two subprograms using the optional parameters IPOTEN 0 or IFORCE 0 to skip the corresponding subprogram execution These parameters can be input in the configuration file as explained below in Section 4 7 In the default case IPOTEN 1 IFORCE 1 both subprograms are executed sequentially in the same run The input files fnames wam config wam and break wam use reserved filenames with the extension wam All of the other input files are identified by three user defined filenames gdf pot and frc These are respectively the filenames used for the Geometry Data File GDF Potential Control File POT and Force Control File FRC Other input output files are assigned the same filenames depending on their context and with different extensions Thus gdf is used for files which relate primarily to a specific body geometry pot to output files from POTEN which are associated with a specific set of inputs in the POT file and fre to output files from FORCE which are associated with a specific set of inputs in the FRC file Some input files are used onl
70. in the GDF file INONUMAP 0 or 1 specifies uniform or nonuniform mapping on the side and bottom of each cylinder The parameters IBOT and IFS specify if a patch is to be included on the bottom IBOT 1 or on the interior free surface IFS 1 IFS 1 should be used if the irregular frequency option IRR 1 is used IBOT 0 can be used in the case of bottom mounted cylinders in which case the draft of each cylinder must be equal to the fluid depth The inputs RADIUS DRAFT XC YC must be included on a separate line for each cylinder The number of patches is NPATCH NCYL 1 IBOT IFS 7 9 MODIFYING THE DLL SUBROUTINE GEOMXACT If a body which is not included in the examples above can be described explicitly by analytic formulae either exactly or to a suitable degree of approximation a corresponding subroutine can be added to the GEOMXACT F file Reference can be made to the source file GEOMXACT F and to the subroutines already provided to understand the appropriate procedures for developing new subroutines A more extensive library of subroutines is available for downloading from www wamit com Users of WAMIT cannot modify the source code in general However GEOMXACT has been separated from the rest of the source code and compiled separately as a dll dynamic link library to be linked to the rest of the executable code at run time Thus users of the PC executable code can modify or extend GEOMXACT for their own applications A similar facility exists fo
71. in the tanks are defined by the parameters ZTANKFS 1 0 99 and ZTANKFS 2 0 01 in the CFG file Thus the height filling ra tios of the tanks are about 99 Except for the roll and pitch moments and corresponding cross coupling coefficients which are affected by the coordinate shift the hydrostatic and hydrodynamic outputs are close to the corresponding values in test22 Since XBODY 3 is nonzero the values of ZTANKFS in body coordinates shown in the header of the output file test22b out differ from the inputs in global coordinates in the CFG file If the assignments of ZTANKFS and or ITRIMWL are removed from the CFG file the tanks will be full including the rigid tops and there will be no free surface effects in the tanks In that case the exciting forces and damping coefficients are unchanged but the added mass coefficients are different Input file test22b cfg TEST22b CFG fpso with 2 interior tanks trimmed to 99 ipltdat 4 ILOWHI 1 ILOG 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 NPTANK 8 12 13 17 RHOTANK 1 0 1 0 relative densities of tank fluids ztankFS 0 99 0 01 ITRIMWL 1 Input file test22b pot test22b pot fpso with 2 interior tanks rigid tops xbody 3 1 2 1 0 1 1 IRAD IDIFF 3 2 0 2 5 3 0 1 NBETA array BETA follows 90 1 NBODY test22b gdf 0 0 0 1 2 0 XBODY 1 1 1 1 1 1 IMODE 1 6 Input file test22b GDF fpso with 2 tanks with rigid tops xbo
72. installed to the subdirectory c wamitv7 testruns Benchmark versions of the output files test out are installed in the subdirectory c wamitv7 testruns out These benchmark output files can be com pared with results obtained by the user to ensure that the software is installed correctly Before running WAMIT with the standard test runs the user needs to open a DOS Command Prompt Window in the WAMIT install directory This can be done by executing wamit bat by selecting Start Programs WAMIT v7 WAMIT v7 or 1 open a DOS Command Prompt Window in the Windows environment a Command Prompt Window is opened by clicking on Start Programs Command Prompt and 2 change to the install directory by entering the command cd wamitv7 Once the DOS command prompt is open and in the WAMIT install directory using either option enter the command cd testruns Since the executable file wamit exe is resident in the directory c wamitv7 the appro 2 6 9 WAMITv7 DEMO Set PSI X Destination Folder Click Next to install to the default folder or dick Change to choose another Install WAMITv7 DEMO to C WAMITV7DEMO Change WI am not using AeroHydro MultiSurf for WAMIT Bak net Cancel Figure 2 6 Installation configuration window for WAMIT DEMO priate command to execute WAMIT is c wamitv7 wamit There are two alternative shortcuts which ma
73. integer in the range 1 6 may be assigned to ISYM Any problem which can be analyzed with the NBODY option can also be analyzed with the generalized mode option If geometric symmetry planes exist for the ensemble of all bodies the use of the generalized mode method is more efficient computationally On the other hand the preparation of input files generally is simpler in the NBODY approach Complex generalized modes can be analyzed by superposition of the separate real and imaginary parts each of which is treated as a separate real mode For example the specifications w7 cos ka wg sin kx define two vertical deflections which can be superposed with a phase difference of 90 to represent a snake like traveling wave along the body Two alternative program units have been provided in the WAMIT software package to facilitate the use of generalized modes The first method also used with previous versions of WAMIT uses a separate program DEFMOD to evaluate the geometric data associated with generalized modes DEFMOD contains a subroutine DEFINE which can be modified by the user to compute the displacement vector for different generalized modes This method can only be used with the low order method ILOWHI 0 The second method which is applicable for both the low order and higher order methods uses a DLL file containing a special subroutine NEWMODES with a library of lower level routines where different types of generalized modes can be
74. is near the panel the panel is subdivided into four smaller panels This subdivision is repeated until the size of the subdivided panel is less than a prescribed multiple of the physical distance from uy to the centroid of the panel For this purpose the size of the panel is defined as the maximum physical length from the center of the panel to its four vertices The maximum size permitted without further subdivision is 1 V2 25 2 3 In some cases a large number of subdivisions are required particularly when uf is close to the sides or vertices of the panel In this case the program terminates subdivision after the domain is subdivided into 2048 subdomains The program issues a warning message to the monitor and error log file but continues without interruption This warning message is most likely to occur when the mapping of a physical surface onto a patch is singular as at the poles of a spherical or spheroidal surface and the accuracy of most relevant hydrodynamic outputs are not affected significantly by this problem In other cases the warning message may be an indication that the geometrical representation of the body surface is defective The singular integral over the square subdomain centered at u is explained below The integration of the dipole is defined in the principal value sense excluding a vanishingly small area around the origin With this definition for the dipole integral both the source and dipole distributions can be eval
75. iterations For large NEQN this is much faster than the methods described below Another advantage of the iterative solver is that it does not require temporary storage proportional to NEQN The direct solver ISOLVE 1 is useful for cases where the iterative solver does not converge or requires a very large number of iterations to achieve convergence The direct solver is based on standard Gauss reduction with partial pivoting The LUD algorithm is employed for efficiency in solving several linear systems simultaneously with different right hand sides The time required for this method is proportional to NEQN In cases where NEQN is relatively small the direct solver can result in reduced computing time particularly if the number of right hand sides is large The direct solver requires sufficient RAM to store at least one complete set of NEQN influence coefficients The block iterative solver ISOLVE gt 2 provides increased options in the solution of the linear system This solver is based on the same algorithm as the iterative solver but local LU decompositions are performed for specified blocks adjacent to the main diagonal Back substitution is performed for each block at each stage of iteration This accelerates the rate of convergence and as the dimension of the blocks increases the limiting case is the same as the direct solver The opposite limit is the case when the dimension of the blocks is one which is the result of setting
76. mapping accounts for the flow singularity near the corner Chapter 8 ANALYSIS OF MULTIPLE BODIES NBODY gt 1 WAMIT includes the capability to analyze multiple bodies which interact hydrodynami cally and mechanically Each of the separate bodies may oscillate independently with up to six degrees of freedom Additional generalized modes can be defined for each body as described in Chapter 9 The bodies may be freely floating fixed or constrained by external forces The basic theory for multibody interactions with waves is similar to that of a single body as described in Chapter 15 The principal extension is to increase the maximum number of degrees of freedom from 6 for a single body to 6N for N bodies N is hereafter used to denote the number of bodies and the index K 1 2 N is used to denote each of the N bodies For example when two bodies are present the maximum possible number of degrees of freedom becomes 12 6 for each body In this example modes 7 8 9 represent translation of body 2 in the direction of the x y and z axes of the coordi nate system fixed on that body These modes correspond to surge sway and heave for the second body respectively Modes 10 11 12 represent rotation about the same axes The extension of this convention to more bodies is evident Thus some output quantities are given in vector or matrix form with dimensions 6N or 6N x 6N respectively Separate GDF files must be input for each body wit
77. must be defined as explained in Chapter 9 to represent the normal velocity of each wavemaker IRAD 0 is recommended with IMODE 1 6 0 to avoid computing the 6 rigid body modes IDIFF 1 is required The separate wavemaker elements are considered to be part of one body with appropriate generalized modes used to represent the independent motion of each element and NBODY 1 No other bodies can be present within the fluid domain The principal outputs are the potential and fluid velocity at specified field points Option 6 If the field point is on the free surface the potential is equivalent to the wave elevation as explained in Chapter 3 No other Options in the FRC file are supported If multiple wavemakers are run together with separate modes for each wavemaker the parameter INUMOPT6 1 should be specified in the cfg file to provide separate outputs for each mode In that case only the complex amplitude is output with a separate pair of columns for each mode as indicated in Section 5 2 A post processor should be used to combine these outputs for arbitrary combinations of simultaneous motion of all wavemakers The subroutine WAVEMAKER is included in the NEWMODES DLL file to analyze one or more wavemakers If IGENMDS 21 is specified in the configuration files the wavemakers 12 10 are hinged with pitching motions about a horizontal axis The depth of this axis is specified in the input file gdf wmkrhinge dat where gdf is the filenam
78. name exists in the model 13 The entity named as tank list is not an Entity List A tank list was specified by name on line 7 of the GDF file but the entity with that name is not an Entity List Check that the second token on line 7 is the correct name for the tank list Entity names are case sensitive Check that an Entity List of this name exists in the model 14 The tank list Entity List isin error A tank list was specified by name on line 7 of the GDF file but the entity with that name is in error An error code will be given this can be looked up in the M ultiSurf manual or help system The most likely cause is that one of the parent lists or surfaces is in error this will result in error 284 on the tank list In the Entities Manager select the tank list and expand the Parents tab to identify the error 15 Tank list contents don t qualify for a tank list A tank list was specified by name on line 7 of the GDF file but the Entity List with that name does not qualify as a tank list Each element of a tank list must be either 1 a surface or 2 an Entity List of surfaces 16 The wetted surface Entity List contains duplicate surfaces Duplicate surfaces in the wetted surface Entities List will lead to singular or very ill conditioned equations in the WAMIT solution Select the Entity List and click on Entities in the left hand column to review its contents Click in the right hand column to edit its contents remove any duplicate
79. numerical integration The control surface is defined in terms of the body coordinate system using the same unit of length The normal vector is defined to point into the interior of the fluid domain between the control surface and the body i e toward the body If part of the control surface coincides with the plane of the free surface the normal on this surface is positive downwards The accuracy of the numerical integration of the momentum flux depends not only on the accuracy of the field quantities on the control surface but also on the discretization of the control surface If a low order control surface is used the integral of the momentum flux is calculated as the sum of the product of the flux at the centroid of each panel and the area of the panel If a higher order control surface is used the control surface is subdivided into higher order panels On each panel the momentum flux is calculated based on third order Gauss quadratures The subdivision of each patch into panels is controlled by the parameters NUC NVC in the same way as the parameters NU NV are used on the body surface See Chapter 7 The input files for the test runs 5 13 and 22 in Appendix A illustrate the different methods for defining the control surfaces Since the description of the control surface in 11 3 FORCE is completely separate from the solution in POTEN arbitrary combinations of ILOWHI in POTEN and ILOWHICSF in FORCE can be used together and
80. of the wave period for all combinations of field points and integration points on the body surface If NFIELD is the number of field points and NBODYSURF is the number of integration points on the body this requires the temporary storage of order NFIELD x NBODYSURF influence functions If NFIELD LARGE 1 is specified in the configuration file the evaluation of the field outputs is skipped in the period loop and performed in a different order after the period loop is completed In this case the loop is over the NFIELD field points and the influence functions are computed within this loop Thus the storage requirement is much smaller If NCPU gt 1 the loop is parallelized This alternative is most efficient if NFIELD is large especially if NPER lt NCPU The best choice between these two options will depend not only on the input parameters but also on the computing system including the number of processors NCPU and size of RAM 14 11 Chapter 15 THEORY In this Chapter the theoretical basis for WAMIT is described Further information can be found in Reference 26 and in the references cited below 15 1 THE BOUNDARY VALUE PROBLEM A three dimensional body interacts with plane progressive waves in water of finite depth H The objective of WAMIT is to evaluate the unsteady hydrodynamic pressure loads and motions of the body as well as the pressure and velocity in the fluid domain The flow is assumed to be potential free of separati
81. of the control surface In this case the file gdf csf is input in the following form header 2 ILOWHICSF fnamel csf fname2 csf Here fname1 and fname2 are the filenames of the two separate CSF files Note that the special value ILOWHICSF 2 is used for this purpose No other data should be included in this file The two separate CSF files are as described in Sections 11 2 and 11 3 except that one file should represent only the inner free surface and the other should represent only the outer surface together with the submerged part of the control surface Both surfaces should meet on the common outer waterline The order of the two files is arbitrary e g fname1 and fname2 can correspond to the inner and outer surfaces or vice versa When two CSF files are used to represent one control surface the symmetry indices ISXCSF and ISYCSF should be the same in both files If ILOWHICSF 1 is used for one or both files the parameter PSZCSF may be assigned independently in each file If PSZCSF is negative the optional csp file should be used to assign the parameters NUC NVC Note that the filename s of the csp file s should be the same as fname1 or fname2 The output files described in Section 11 6 for visualization of the control surfaces and for low order control surfaces correspond to the complete control surface with the same filename as the gdf file Thus these output files are the same as in the case where only one CSF file is used 11
82. of the two patches The parameter NV is the same as the corresponding exterior parameter either NU or NV depending on the orientation of the exterior patch so the panel subdivisions are the same along the waterline The spline control parameters for the interior patches are displayed in the header of the OUT file when NBODY 1 following the panels of the exterior body surface However when NBODY gt 1 these parameters are not output When the program connects adjacent sides of patches in the waterline the patches are identified based on the coincidence or close proximity of their vertices The parameter TOLGAPWL is used for this purpose to allow for small gaps or overlaps between adjacent patches at the waterline The default value TOLGAPWL 10 is used unless a different value of this parameter is defined in the CFG file as explained in Section 3 7 In the test for adjacent patches the nondimensional Cartesian coordinates of the adjacent patch corners are evaluated and the distance between these points is computed The patches are assumed to be connected if this distance is less than either TOLGAPWL or the product of TOLGAPWL and the maximum length of one of the patch sides The latter value is introduced to allow for cases where the size of the structure is much larger than the characteristic length ULEN The default value is recommended in general If the program is unable to close a waterline using this value an error message is displayed s
83. on the bottom and interior free surface When the nonuniform mapping option is selected the vertical coordinate on the side is a cubic polynomial in V and the radial coordinate on the other patches is a quadratic polynomial in V such that the first derivatives vanish at the corner and at the intersection of the side and free surface This nonuniform mapping is analogous to the use of cosine spacing in the low order panel method to achieve a finer discretization of the solution near these boundaries The motivation for using the nonuniform mapping option is discussed in Appendix A 11 where both options are compared and in more detail in Reference 25 The code in the subroutine CIRCCYL may be used as a guide for other geometries where nonuniform mapping is desirable Before using this GDF file the user should assign appropriate values for the parameters ULEN GRAV RADIUS DRAFT INONUMAP and an appropriate header As noted in Section 4 10 this data must be contained within columns 1 80 of the GDF file In the normal case described above NPATCH 2 corresponding to the side and bottom of the cylinder Two other situations exist where the same subroutine can be used 1 for a bottom mounted cylinder NPATCH 1 and DRAFT is assigned with the same value as the fluid depth HBOT and 2 if NPATCH 3 the interior free surface is included to permit the removal of irregular frequency effects IRR 1 as described in Chapter 10 The restriction DRAFT
84. only the sine transform of radiation irf s IOUTFCFS 0 or any other integer except 1 or 2 output both cosine and sine trans forms These transforms are redundant as explained below The value IOUTFCFS 0 is recom mended except in cases involving a large number of radiation modes where the number of columns in the _JR1 output files may be excessive Line 7 contains the optional parameters ULEN and GRAV which are the same char acteristic length scale and gravitational acceleration parameters as input in the GDF file These parameters are only required when Options 5 or 6 are included and when the ra diation outputs are specified as explained in Section 13 5 In all other circumstances the parameters ULEN and GRAV can be omitted from inputs f2t When ULEN and GRAV are included in inputs f2t it is essential to also include IOUTFCFS on line 6 The use of the special file inputs f2t is optional If this file does not exist or if the first five lines cannot be read with the appropriate data the user is prompted to specify all of the above inputs interactively The special file can also be used in a partial form with some but not all of the above lines but the lines included must be in the same order as above This permits the user to interactively input different values of the time step and number simply by omitting Line 5 from the special file 13 4 The numeric data in the special file is read with free format READ statements sepa r
85. output files 5 3 Froude Krylov and scattering forces 5 4 Body pressure for the higher order method 5 5 Body pressure and velocity at specified points 5 6 Auxiliary files for hydrostatics hst and external forces mmx 5 7 Auxiliary output files for the geometry 5 8 Error messages 5 9 The log file wamitlog txt 5 10 The intermediate data transfer file p2f THE LOW ORDER METHOD ILOWHI 0 6 1 The Geometric Data File GDF 6 2 Use of the source formulation ISOR 1 6 3 Bodies with thin submerged elements THE HIGHER ORDER METHOD ILOWHI 1 7 1 Subdivision of the body surface in patches and panels 7 2 B Spline representation of the solution 7 3 Order of Gauss Quadratures 7 4 The Geometric Data File 7 5 Geometry represented by low order panels IGDEF 0 7 6 Geometry represented by B Splines IGDE 7 7 Geometry represented by MultiSurf IGDEF 7 8 Analytic representation of the geometry 7 9 Modifying the DLL Subroutine GEOMXACT 7 10 Bodies with thin submerged elements 7 11 The Optional Spline Control File 7 12 The use of default values to simplify inputs 713 Advantages and disadvantages of the higher order method ANALYSIS OF MULTIPLE BODIES NBODY gt 1 8 1 ne to POBLE tda f a2 I Order Method he DLL Subroutine NEWMODES 9 4 Hydrostatics 9 5 NBODY Analysis 10 USE OF IRREGULAR FREQUENCY OPTION IRR gt 0 10 1 Input parameters 10 2 Automatic free surface discretiz
86. patches in the GDF file is not supported in Version 7 NPFORCE is an integer array used to specify the panels or patches which are included in the integrations of the pressure force and moment The data in this array are in pairs with the same format rules as specified below for NPFSP Further details are given in Section 12 6 NPFSP is an integer array used to specify the panel or patch indices of free surface pressure surfaces The data in this array are in pairs denoting the first and last index for each surface An even number of indices must be included on each line Each pair of indices must be enclosed in parentheses as shown in the input file test17c cfg More than one line can be used for multiple surfaces and or multiple surfaces can be defined on the same line Only integer data and parentheses are read for the array NPFSP with spaces or other characters separating each index Other ASCII characters may be used in addition to the integers and parenthesis but integers and parenthesis must be used only for the inputs above Further details are given in Section 12 5 NPNOFORCE is an integer array used to specify the panels or patches which are not included in the integrations of the pressure force and moment The data in this array are in pairs with the same format rules as specified above for NPFSP Further details are given in Section 12 6 NPTANK is an integer array used to specify the panel or patch indices of internal tanks Th
87. program These options are described in Sections 10 2 4 below When NBODY gt 1 different values of IRR may be assigned for each body following the format in Section 8 4 More specific information is given in Section 10 5 If IRR 1 in the low order method ILOWHI 0 the user must discretize the free surface The coordinates of these panel vertices are included in the GDF file The vertices of the free surface panels must be numbered in the clockwise direction when the panel is viewed from inside the body or in the counter clockwise direction when the panel is viewed from above the free surface The whole half or a quadrant of the interior free surface must be discretized in accordance with the discretization of the body surface when there is geometric symmetry The number of panels the parameter NPAN in the GDF file is the sum of the number of panels on the wetted surface of the body and the interior free surface The order of the indices for the body panels and free surface panels is not restricted in Version 7 If IRR 1 in the higher order method ILOWHI 1 the user must represent the interior free surface with one or more patches in the same manner as for the body surface This must be done with the normal pointing downward in the negative z direction In the context of the right hand rule stated in Section 7 1 this is equivalent to requiring that the parametric coordinates u v for the free surface patch are defined such that the positi
88. response amplitude of each mode is included in the RAO s In TEST16 the subroutine BARGE IGDEF 5 is used The half length half beam and draft are specified in TEST16 GDF In TEST16a the option IGDEF 0 is used with the vertices of the patches specified in TEST16a GDF in the same format as for low order panels Input file testi6 cfg TEST16 CFG elastic barge with 8 beam modes ipltdat 5 ilowgdf 5 ILOWHI 1 IALTFRC 2 ISOLVE 1 IQUADI 5 IQUADO 4 MONITR 0 NUMHDR 1 IGENMDS 16 NEWMDS 8 Input file test16 pot TEST16 elastic barge with 8 beam modes 0 0 IRAD IDIFF 2 NPER array PER follows 7 8 1 NBETA array BETA follows 180 1 NBODY test16 gdf 0 0 0 0 XBODY 1 0O 1 0O 1 0 IMODE 1 6 Input file test16 gdf TEST16 elastic barge 1 9 80665 ULEN GRAV 1 i ISX ISY 3 5 NPATCH IGDEF 1 NLINES 40 0 5 0 5 0 half length half beam draft Input file testi6 spl TEST16 elastic barge 3 3 NU NV end 4 4 KU KV 5 2 side 4 4 5 2 bottom 4 4 3 in config wam 4 in config wam IQUO IQVO are not specified IQUADO IQUI IQVI are not specified IQUADI test16 frc TEST16 elastic barge with 8 beam modes Input file 0 0 0 0 0 1 1000 O 4 00000E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 13333E 09 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0
89. results with and without irregular frequency removal then you have to be sure that the patches to be excluded are the last in patch order There are two rules governing the order of patches corresponding to the two alternatives for the Entity List 1 If you usean explicit Entity List the patch order will be the order in which the surfaces are listed in the Entity List 2 If you use the default identifier for the Entity List the patch order will be the order of surfaces in the MS2 file You can find out this order by searching for Surf in Edit Model File or Notepad In MultiSurf another alternative is to turn on only the Surfaces filter set Select Visible to on Sdect All and read the order in the Selection Set M anager 4 4 Surface normal orientations For a proper solution of the potential boundary value problem WAMIT requires that the positive normal to each surface be directed into the body A patch closing the top of the body for irregular frequency removal must have its normal directed downward again into the body The positive normal in WAM IT is calculated as the cross product Ox u x Ox v Normalized to unit length If normals are backwards on some surfaces WAMIT s calculation of volumes will very likely show discrepancies between the X Y and Z directions If all normals are reversed the 3 volumes will agree but will be negative And the hydrodynamic solution probably won t make much sense
90. saved in a binary P2F file Thus it is possible to make multiple runs with FORCE varying the requested parameters to be output without re running POTEN in each instance The evaluation of drift forces using a control surface is an exception where the computational burden in FORCE may be greater than that in POTEN Figure 1 1 shows the architecture of the two subprograms and the principal input output files For simplification this figure does not include additional input files required for the case of multiple bodies the optional spline control file which may be used to vary B spline parameters in the higher order analysis and output files which log errors warnings and other auxiliary data The analysis for the generalized modes also requires an additional input file or special subroutine to define the user specified modes Figure 9 1 in Chapter 9 shows the flow chart of POTEN for this case 1 5 ofg cfg potpot Figure 1 1 Flow chart of WAMIT showing the subprograms POTEN and FORCE with their associated input and output files Filenames in italics are specified by the user The four primary input files and optional configuration files described in Chapters 4 6 and 7 are indicated in the left hand column The names of these files are prescribed either by the optional file FNAMES WAM or by the interactive inputs represented by the top and bottom arrows in the right hand column Additional input files which may be required
91. submerged One quadrant of the surface is represented by one patch If the torus is floating and NPATCH 2 the free surface inside the moonpool is represented by an additional patch as in CYLMP TLP defines a generic tension leg platform TLP with four circular columns connected by rectangular pontoons The bottom surfaces of the columns and pontoons are at the same draft and the columns are equally spaced in a square array The quadrant is defined to include one column and half of the adjoining pontoons The column radius RADIUS and draft DRAFT and a half of the horizontal spacing between the axes of adjacent columns HSPACE are specified on one line of the GDF file The pontoon width WIDTH and height HEIGHT are specified on a separate line The width of the pontoons is restricted so that they do not intersect off the columns In the special case WIDTH RADIUSxv2 the pontoon corners coincide on the column and NPATCH 11 This includes eight patches on the top sides and bottom of the pontoons one patch on the column above the pontoons one patch on the column outside the pontoons and one patch on the column bottom In the general case WIDTH lt RADIUSx v2 NPATCH 12 with the 12th patch on the column between the inside corners of adjacent pontoons This case is illustrated in the test run TEST14 SEMISUB defines a generic semi submersible with two rectangular pontoons and NCOL equally spaced circular columns on each pontoon The pontoon dimensi
92. test runs with trimmed waterlines TESTO1A TESTO9A TEST13A and TEST22A The perspective plots which accompany these descriptions il lustrate the trimmed conditions of the structures When multiple bodies are analyzed the vector XTRIM must be input separately for each body following the same format as for XBODY in Section 8 4 TEST13A illustrates this procedure for NBODY 2 The following coordinate systems and input parameters should be considered in defining the process of trimming waterlines X Y Z are global coordinates with Z 0 in the plane of the free surface x y z are conventional body coordinates which define the submerged body surface in WAMIT 7 referred to hereafter as GDF coordinates are the coordinates used to define the body geometry in the GDF file In the low order method ILOWHI 0 when the panel vertices are input from the GDF file these are converted from GDF coordinates to body coordinates using the translation and rotations defined by XTRIM When the higher order method is used ILOWHI 1 12 6 the same coordinate transformations are performed from the subroutine outputs each time that the subroutine defining the body surface is called The practical effect in both cases is that the original definition of the body geometry in the GDF file is replaced during the WAMIT computations by a new transformed description in x y z coordinates which represents only the submerged portion of the b
93. the appropriate WAMIT output files are available The user must specify the filenames of these files and a small number of input parameters either interactively in response to appropriate runtime prompts or by preparing the special input file inputs f2t The following example of this special input file corresponds to the TEST 14a test run TEST 14a described in Appendix A header line for inputs f2t control file TLP example TEST14a O O 1 IRAD IDIFF NUMHDR O O 2 CINUMOPTS INUMOPT6 IPEROUT 0 2 100 DT NT time step and number of time steps O IOUTFCFS output both cosine and sine transforms 43 125 9 80665 ULEN GRAV These inputs are described for each line as follows Line 1 is an ASCII header dimensioned CHARACTER 72 as in most WAMIT input files This line should be used to insert a brief description of the file Line 2 is a list of the filenames not the extensions of the primary and secondary WAMIT output files F2T attempts to open all numeric output files with the same file names and includes all of these files in the analysis Thus the determination of which 13 3 options to be included depends on the available WAMIT output files In this example where the TEST14a FRC control file was used as in the standard WAMIT test runs Op tions 1 2 3 4 are included in the F2T analysis If all of the input data is included in the primary file it is not necessary to list other filenames Additional secondary files can also be included up
94. the mean force and moment from momentum integration only for unidirectional waves IOPTN 8 2 output the mean force and moment from momentum integration for all combinations of wave headings IOPTN 9 IOPTN 9 0 do not output the mean force and moment from pressure integration IOPTN 9 1 output the mean force and moment from pressure integration only for unidirectional waves IOPTN 9 2 output the mean force and moment from pressure integration for all combinations of wave headings The options IOPTN 6 lt 0 apply only for the low order method ILOWHI 0 and require the source formulation ISOR 1 If the low order method is used the options IOPTN 5 gt 1 and IOPTN 9 gt 0 require the source formulation ISOR 1 The settings of the indices IOPTN I must be consistent with themselves and with 4 14 the indices IRAD IDIFF and NBETA set in the Potential Control File Error messages are generated if inconsistent indices are input Otherwise the indices IRAD IDIFF and IOPTN D I 1 9 can be selected in any way the particular application may suggest Three principal applications are as follows Forced motions in calm water the radiation problem In this case the modes of motion are specified by the MODE indices in the POT file The diffraction index IDIFF should be set equal to 1 In the FRC file the indices IOTPTN 2 4 should be set equal to zero The corresponding linear force coefficients are obtained with Option 1 Fie
95. the output file gdf LOW GDF The default value is ILOWGDF 0 ILOWH is an integer parameter specifying the use of the low order or higher order panel method ILOWHI 0 Low order panel method Chapter 6 ILOWHI 1 Higher order panel method Chapter 7 IMODESFSP is an integer parameter specifying the subroutine used to define pressure distributions on interior free surfaces of the body see Section 12 5 INUMOPTS5 is an integer parameter specifying the option to evaluate the separate radi ation and diffraction components of the body pressure and velocity see Sections 3 5 and at INUMOPT5 0 output the total body pressure and velocity INUMOPT5 1 output the total body pressure and velocity in the formatted output file out Output the separate components in the numeric output files 5p 5vx 5vy 5vz INUMOPTG6 is an integer parameter specifying the option to evaluate the separate radi ation and diffraction components of the pressure and velocity at field points see Sections 3 5 and 3 7 INUMOPT6 0 output the total field pressure and velocity INUMOPT6 1 output the total field pressure and velocity in the formatted output file out Output the separate components in the numeric output files 6p 6vx 6vy 6vz IOUTFNAME is an integer parameter specifying the filename of the output files see Section 5 1 IOUTFNAME 1 Append N to the filename 1 lt N lt 9 IOUTFNAME 2 Append NN to the filename 1 lt
96. the same manner as IGDEF to select the appropriate subroutine Any of the existing subroutines which are normally used to define body geometry can be used to define the control surface for example specifying ICDEF 1 defines the control surface as a circular cylinder with spec ified radius and draft It is important to use different subroutines for the body geometry and control surface with ICDEF4IGDEF The reason for this restriction is that when parameters are input by the same subroutine from the GDF file and CSF file these param eters may be overwritten If it is desired to use the same subroutine for both geometries a duplicate copy of the subroutine with a different name and assigned value of IGDEF should be added to GEOMXACT PSZCSF is a parameter which controls the accuracy of the numerical integration over the control surface in the same manner that PANEL_SIZE is used on the body cf Chapter 7 Thus the control surface is subdivided into elements with the approximate length scale of each element equal to PSZCSF If the parameter PSZCSF is negative the subdivision of the control surface is determined by the parameters NUC NVC in the file gdf CSP in an analogous manner to the use of the parameters NU NV in the spline control file gdf SPL Section 7 11 TEST22 is an example where the latter procedure is used Four special CSF subroutines are included in the standard GEOMXACT F and GE OMXACT DLL files to define control surfaces in
97. to RAM is much faster this option is advantageous from the standpoint of computing time if sufficient RAM is available Section 14 4 describes the procedure to allocate the data storage between RAM and the hard disk in an efficient manner Section 14 5 explains details associated with the use of scratch files on the hard disk The advantages and use of multiple processors are described in Section 14 6 including a comparison of computing times for two applications This shows the dramatic reduction in computing time that can be achieved when the number of CPUs is increased However the use of multiple CPUs requires a proportionally large size of RAM Section 14 7 gives instructions for users to modify the WAMIT DLL files geomxact and newmodes Section 14 8 lists the filenames which are reserved for use by WAMIT 14 1 NUMBER OF EQUATIONS NEQN AND LEFT HAND SIDES NLHS In the low order method ILOWHI 0 the number of equations depends on the number of panels NPAN specified in the GDF input file s In the higher order method ILOWHI 1 NEQN depends on the number of patches and on the spline paramters NU NV KU and KV NEQN is modified if the body geometry is reflected about planes of symmetry auto matic discretization of the interior free surface is utilized IRR gt 1 or waterline trimming is used ITRIWMWL 1 The value of NEQN for each run is listed in the header of the out output file Typical values of NEQN are between 100 and 10 000
98. to a maximum limit of 256 ASCII characters for the complete line At least one blank space must be used to separate each filename Lines 3 and 4 contain the six control parameters identified by the comments in parenthe sis These parameters must have the same values as in the WAMIT runs No distinction is made between IRAD IDIFF 0 or 1 and the only important value to specify correctly is 1 For any input values of IRAD IDIFF other than 1 the results are the same as for 0 or 1 NUMHDR which is optional in WAMIT with the default value 0 must be specified here with the value 0 no headers or 1 one line of headers to indicate the pres ence or absence of a header line in the WAMIT numeric output files INUMOPT5 and INUMOPT6 must be specified here with the value 0 default or the separate components values 1 IPEROUT 1 or 2 must be specified to distinguish wave periods and frequencies in the WAMIT output files Line 5 contains the time step and number of time steps for the computation and tab ulation of the time domain response functions The radiation IRF S are computed and tabulated for t 0 and for NT positive times DT 2DT 3DT NT DT The diffrac tion IRFs are evaluated for both positive and negative times starting with NT DT and ending with NTxDT Line 6 contains the optional parameter IOUTFCFS with the following options for its value IOUTFCFS 1 output only the cosine transform of radiation irf s IOUTFCFS 2 output
99. to the POTEN subprogram The name of this file can be any legal filename accepted by the operating system with a maximum length of 16 ASCII characters followed by the extension pot In Version 7 the following format is used for the data in this file header HBOT IRAD IDIFF NPER PER 1 PER 2 PER 3 PER NPER NBETA BETA 1 BETA 2 BETA 3 BETA NBETA NBODY GDF 1 XBODY 1 1 XBODY 2 1 XBODY 3 1 XBODY 4 1 MODE 1 1 MODE 2 1 MODE 3 1 MODE 4 1 MODE 5 1 MODE 6 1 GDF 2 XBODY 1 2 XBODY 2 2 XBODY 3 2 XBODY 4 2 MODE 1 2 MODE 2 2 MODE 3 2 MODE 4 2 MODE 5 2 MODE 6 2 GDF NBODY XBODY 1 NBODY XBODY 2 NBODY XBODY 3 NBODY XBODY 4 NBODY MODE 1 NBODY MODE 2 NBODY MODE 3 NBODY MODE 6 NBODY The data shown on each line above is read consecutively by corresponding read state ments Thus it is necessary to preserve the line breaks indicated above but if a large number of periods PER and or wave heading angles BETA are input these may be placed on an arbitrary number of consecutive lines The definition of each variable in the Potential Control File is as follows header denotes a one line ASCII header dimensioned CHARACTERx72 This line is available for the user to insert a brief description of the file with a maximum length of 72 characters including leading blanks HBOT is the dimensional water depth By convention in WAMIT a value of HBOT less than or equal to zero is interpret
100. total pressure is the same as the diffraction pressure if IRAD 1 the diffraction pressure is not output in this case The radiation pressure coefficient is output when IRAD gt 1 The data in the 5pb file is useful for special post processing purposes such as for interfacing with structural loads analyses The content of the 5pb numeric output file is listed below hhh moved up to top of list to avoid blank line HEADER ISX ISY ULEN NPATCH IRAD IDIFF NPER NBETA 5 5 NEQN NLHS NDFR NBODY XBODY L J L 1 4 J 1 NBODY XBCS L J L 1 2 J 1 NBODY IBPTH L L 1 NPATCH IBMOD L L 1 NBODY IGEO J J 1 8 CILHS J J 1 4 IFLAT L L 1 NPATCH KU L KV L NUCL NV L L 1 NPATCH NMDS J J 1 4 ICOL J J 1 NDFR MDS L J L 1 NDFR J 1 4 BETA NB NB 1 NBETA omit if IDIFF 1 Loop over number of periods repeat NPER times PER WVNFIN WVNUM IFREQ IF block starts if IFREQ 0 IF block starts if IRAD gt 1 and IDIFF gt 1 Loop over wave headings starts repeat NBETA times WRAO IM NB IM 1 NDFR Loop over wave headings ends repeat NBETA times Loop over wave headings starts repeat NBETA times Loop over number of symmetric images repeat MXNLHS times Loop over number of patches repeat NPATCH times WPRS I M NB I NP 1 NQ omit if IFLAT L 1 End of the loop over number of patches End of the loop over symmetric images Loop over wave headings ends repeat NBETA ti
101. txt 1 7 e Several changes have been introduced to simplify the input files and to use a more consistent notation for the numeric output files See Section 4 1 e The configuration parameter IPERIO has been replaced by two parameters IPERIN IPEROUT to control the definitions of both the input and output of the wave period array See Section 4 7 e The auxiliary output file mmx has been added to output external force matrices mass damping stiffness and other quantities used for post processing See Section 5 6 E 1 3 CHANGES INTRODUCED IN Version 7 1 New features which are included starting in Version 7 1 are outlined below e The configuration parameter IDELFILES can be used to skip interactive prompts and delete or overwrite old p2f files see Section 4 7 and Section 4 9 e The configuration parameter IOUTFNAME can be used to assign unique filenames to output files see Section 4 7 and Section 4 9 e The configuration parameter IOUTLOG can be used to assign the output filename to the log file wamitlog txt see Section 4 7 and Section 4 9 e The configuration parameters NPFORCE and NPNOFORCE can be used to specify the set of panels or patches which are included or omitted in the integration of the hydrodynamic pressure forces see Section 4 7 and Section 12 6 e The configuration parameter TOLFPTWL can be used to adjust the tolerance for field points close to waterlines and to omit field points which are inside the
102. u or x v vanishes or because they have the same direction The most commonly encountered coordinate singularity is a pole where one or the other of 6x du 0x dv vanishes along one whole edge of the parameter space e g the type of singularity at the north and south poles of a sphere that is parameterized by latitude and longitude There are many ways to create surfaces with poles and other coordinate singularities in MultiSurf for example when a RuledSurf is made between a curve and a point a pole occurs at the point Some kinds of coordinate singularities are associated with numerical ill conditioning in WAMIT and so should be avoided as much as possible in modeling for RG2WAMIT There are situations where coordinate singularities are apparently harmless e g the south pole of a half submerged sphere or the south pole of a truncated vertical cylinder There are other situations where a coordinate singularity is distinctly beneficial See the remarks below under Cosine spacing WAMIT Inc is recommending especially against poles on the free surface or at chines i e sharp edges that protrude into the water such as the junction between side and bottom surfaces of a truncated vertical cylinder 4 12 Breaklines in surfaces The RGKerndl versions used in RG2WAMIT and MultiSurf recognize the presence of breakpoints in curves and breaklines in surfaces A breakpoint is a place where a curve has a di
103. velocity potentials are obtained for each wave period a 2 7 new line of information is displayed including the wave period time and the maximum number of iterations required for the radiation and diffraction solutions After the first wave period the computational time required for each subsequent period is reduced since the integration of the Rankine components of the source potential are evaluated initially and saved for reuse After the last period the file test01 p2f is saved on the disk storing the velocity potentials and other inputs to the subprogram FORCE Output from FORCE will appear relatively quickly on the screen and the same output is stored in the file test01 out The latter file includes useful identification information concerning the inputs body parameters run times and dates This is followed for each period by tabulations of the hydrodynamic parameters requested in test01 frc Assuming the standard version of test01 out has been saved in a subdirectory as recommended in Section 2 1 the data in the new version of test01 out can be compared with the standard file with the same name On a contemporary PC the total run time for TESTO1 should be a few seconds 2 5 RUNNING TEST11 TEST11 is intended to complement TESTO1 using the higher order method of solution ILOWHI 1 The body dimensions and other inputs are the same but the surface of the cylinder and the solution for the velocity potential are represented in a more acc
104. 0 0 0 0 O 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 6 25705E 06 0 0 0 0 O 0 0 0 0 0 0 0 0 0 4 75441E 07 0 0 0 O O 0 1 82720E 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 99297E 08 0 0 0 O 0 0 0 0 0 0 0 0 1 11419E 09 0 O O 0 0 0 0 0 0 0 0 0 0 0 2 17352E 09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 85260E 09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 35602E 09 0 0 0 0 0 0 0 0 0 0 Input file testi6a pot TEST16a elastic barge with 8 beam modes igdef 0 a 0 0 IRAD IDIFF 2 NPER array PER follows 7 8 1 NBETA array BETA follows 180 1 NBODY testl6a gdf 0 0 0 0 XBODY 1 O 1 O 1 0 IMODE 1 6 First 10 lines of input file testl6a gdf TEST16a elastic barge with 8 beam modes igdef 0 3 flat panels 1 0000 9 80665 aL 1 0 NPATCH IGDEF 40 0000 0 000000 5 00000 40 0000 5 00000 5 00000 40 0000 5 00000 0 000000 40 0000 0 000000 0 000000 end 40 0000 5 00000 5 00000 0 000000 5 0
105. 0 O 8 0201552E7 0 O O 0 O O 9 54906731E7 0 IDAMP 0 ISTIFF 0 NBETAH 0 NFIELD A 15 SEMI SUB TEST15 The subroutine SEMISUB IGDEF 10 is used to generate a Semi submersible with the dimensions specified in TEST15 GDF There are five columns on each pontoon as shown in the figures below For this structure a total of 10 patches are required If NPATCH 11 extensions of the pontoons can be included as explained in the subroutine comments Option 7 is used to evaluate the drift force and moment from the method described in Chapter 11 The control surface is defined by the program using the automatic method described in Section 11 4 with the input parameters specified in the CSF file The outer control surface is a rectangular box and three inner partitions are defined to separate the columns as discussed in Example 4 of Section 11 4 A a Input file testi5 cfg TEST15 CFG Semi sub with five columns on each pontoon ipltdat 1 ISOLVE 1 NUMHDR 1 KSPLIN 3 IQUADI 4 IQUADO 3 ILOWHI 1 Input file test15 pot TEST15 Semi sub with five columns on each pontoon zl 0 0 IRAD IDIFF 1 NPER array PER follows 18 0 1 NBETA array BETA follows 180 1 NBODY test15 gdf 0 0 0 0 XBODY O O 10 1 0 IMODE 1 6 Input file test15 gdf TEST15 Semi sub NCOL 5 IGDEF 10 1 9 80665 ULEN GRAV 1 1 ISX ISY 10 10 NPATCH IGDEF 2 NLINES 260 20 40 30 20 XL Y1 Y2 Z1 Z2 60 8 5 DCOL RCOL NCOL In
106. 0 0 0 INONUMAP XBODY 3 2 000000 0 000000 1 000000 2 000000 2 100000 1 000000 2 000000 2 100000 0 100000 2 000000 0 000000 0 100000 patch8 tanki fwd 000000 000000 000000 000000 000000 000000 0 000000 0 000000 0 000000 0 000000 0 000000 000000 000000 2 0 0 2 000000 0 2 2 000000 000000 2 000000 2 000000 0 000000 2 000000 0 000000 0 000000 2 000000 2 000000 2 000000 2 000000 2 000000 Input file 0 0 0 000000 0 0 TEST22 SPL 4 OOo OU wwwN O os 3 ONNWNHNNWHEN W WD 100000 100000 100000 100000 000000 000000 100000 100000 000000 100000 100000 000000 000000 100000 100000 000000 100000 100000 100000 100000 000000 000000 100000 100000 000000 100000 100000 000000 ONNONNDONNNNONNDCOUONNODONNVDVDAONNNN test22 spl FPSO with two tanks 000000 000000 100000 100000 100000 100000 100000 100000 100000 100000 000000 000000 000000 000000 100000 100000 000000 000000 100000 100000 100000 100000 100000 100000 100000 100000 000000 000000 patch9 tanki side patchi0 patchil patchi2 patchi3 patchi4 patchi5 tank1 tanki tank2 tank2 tank2 tank2 bot aft fwd side bot aft 3 3 3 2 Input file test22 frc TEST22 FRC fpso with 2 tanks one field point on free sur
107. 0 00 IOPTN 1 9 0 000000 VCG 2 500000 0000000 0000000 0000000 5 000000 0000000 0000000 0000000 5 000000 XPRDCT 0 NBETAH 0 NFIELD Appendix B FILE CONVERSION USING THE UTILITY V6V7inp The utility executable program V6V7inp is supplied with WAMIT Version 7 to facilitate the conversion of old input files from Version 6 to Version 7 These changes are summarized in Section 4 1 This program is intended for use on Windows PC s Reference will be made here to directories folders and sub directories which are adjacent to the directories The program is intended to process one or more sets of input files identified by correspond ing FNAMES WAM files as described in Section 4 8 These are referred to here as the fnames files which should all have the extension wam but may have different filenames corresponding to different sets of input files as with the standard test runs described in Appendix A The program requires the same Intel Microsoft DLL files as are required by WAMIT Version 7 listed in Section 2 1 These must be in the same directory as the program at runtime The program can either be run locally from each directory where input files are processed or alternatively and more conveniently in one directory of the PC which is identified in the system PATH Before executing the program two preparations must be made 1 a sub directory V7inp should be made to save the new input files and
108. 000 Input fi le test01 frc TESTO1 FRC Circular cylinder ILOWHI 0 IRR 0 1 1 0 000000 1 000000 0000000 0000000 H HH NO oo So 1 1 0 0000000 1 000000 0000000 3 0 2 1 0000000 0000000 1 000000 VCG XPRDCT NBETAH NFIELD XFIELD Input file testOla cfg TESTO1A CFG cylinder R 1 T 0 5 trimmed waterline ilowgdf 1 ipltdat 5 ISOR 1 omit ISOR in POT file include source formulation ISOLVE 0 use iterative solver ISCATT 0 solve for total diffraction potential not scattering ILOG 1 omit ILOG in POT file integrate log singularity IRR 0 omit IRR in POT file no irregular frequency removal MONITR 0 do not write FORCE output data to monitor NUMHDR 1 write headers to numeric output files ITRIMWL 1 XTRIM 0 27 0 0 15 Input file testOla pot TESTO1A POT cylinder R 1 T 0 5 trimmed waterline i HBOT 1 1 IRAD IDIFF 3 NPER array PER follows 8 971402 2 006403 1 003033 PER 1 NBETA array BETA follows O BETA 1 NBODY test01 gdf 0 0 0 0 HBOT XBODY 1 4 tod DAM IMODE 1 6 Input file testOla frc TESTO1A FRC Circular cylinder trimmed waterline 1 1 1 1 0 3 0 2 0 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 5 0 0 1 5 0 0 5 XFIELD A 2 IRREGULAR FREQUENCY REMOVAL TEST02 This test run illustrates the use of the irregular frequency option described i
109. 0000 5 00000 Input file testi6a spl TEST16A elastic barge with igdef 0 patches defined by flat panels 3 NU NV end 3 4 4 KU KV 5 2 side 4 4 5 2 bottom 4 4 testl6a frc TESTi6a elastic barge with 8 beam modes igdef Input file 0 0 0 0 0 0 1 1000 0 0 0 4 00000E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 13333E 09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 1 E 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 6 25705E 06 0 0 0 O 0 0 0 0 0 0 0 0 0 0 4 75441E 07 0 0 0 0 O 0 0 0 0 0 0 0 0 0 1 82720E 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 99297E 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 11419E 09 0 O O 0 0 0 0 0 0 0 0 0 0 0 2 17352E 09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 85260E 09 0 0 0 0 0 0 0 0 0 0 0 0
110. 00000 100000 100000 000000 000000 100000 100000 000000 100000 100000 000000 000000 100000 100000 000000 100000 100000 100000 100000 000000 000000 100000 100000 000000 100000 100000 000000 ONNONNDOUONNNNONNDAOUONNODONNGCONNNNON N test22a spl TEST22a SPL FPSO with two tanks 4 3 COCO wow NO A WNHNNWHREN WN 000000 100000 100000 000000 000000 100000 100000 100000 100000 100000 100000 100000 100000 000000 000000 000000 000000 10000 10000 000000 000000 10000 10000 10000 10000 10000 10000 10000 10000 000000 000000 patch8 tanki fwd patch9 tanki side patchiO tanki bot patchi1 tanki aft patchi2 tank2 fwd patchi3 tank2 side patchi4 tank2 bot patchi5 tank2 aft trimmed waterline w w www NUONNNY Input file test22a frc TEST22A FRC fpso with 2 tanks one field point on free surface in each tank 1 1 1 1 0 3 0 1 1 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 1 0 1 0 1 0 2 1 0 1 0 0 0 In test22b the origin of the coordinate system is shifted to the bottom of the keel with XBODY 3 1 2 assigned in the POT file and also in the GDF file The geom etry is unchanged from TEST22 except that the tops of the tanks are defined by two extra patches and the free surface elevations
111. 00000 1 000000 0000000 0000000 0000000 1 000000 0 2 1 5 0 0 0 0 1 5 0 0 0 5 A 3 LOCAL PRESSURE DRIFT FORCE TESTOS This test run is used to illustrate the use of the source formulation Section 5 2 to de termine the mean drift force and moment from local pressure integration The motions and the drift forces are evaluated for a freely floating truncated vertical circular cylinder of radius 1 meter and draft 1 meter in a water depth of 7 14 meter for four wave periods and one wave heading The origin of the global coordinate system is located at the intersection of the vertical axis of the cylinder and the undisturbed position of the free surface The origin of the body fixed coordinate system is shifted 0 515 meters under the free surface Using two planes of symmetry the first quadrant of the surface of the cylinder is discretized with 288 panels 12 8 and 16 panels are distributed in the azimuthal radial and vertical directions with cosine spacing at the free surface and corner The characteristic length is set equal to the radius of the cylinder The cylinder center of gravity is located at the origin of the body coordinate system and the radii of gyration relative to its axes are shown in the FRC file Generally speaking the evaluation of mean drift forces is more accurate when the momentum conservation method is used since this does not depend on local velocities on the body surface However the momentum method can
112. 00000 25 00000 0000000 0000000 0000000 25 00000 XPRDCT 0 NBETAH 0 NFIELD First 10 lines of input file test20 bpi bpi input file for test20 body pressure points for MultiSurf barge 556 44 7760 0 0000 1 0074 42 9240 0 0001 1 8961 45 0680 0 2891 0 8477 43 5610 0 6874 1 6131 45 3540 0 5549 0 6847 44 1780 1 2902 1 3169 40 8950 0 0006 2 6665 38 6880 0 0006 3 3185 A 21 SPAR WITH THREE STRAKES TEST21 The subroutine SPAR IGDEF 12 is used to generate the SPAR with three strakes with the dimensions specified in TEST21 GDF Except for the geometry the inputs correspond to the low order test runs TEST09 Input file test21 cfg TEST21 CFG SPAR with three strakes ipltdat 4 ilowgdf 4 ILOWHI 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 IPERIN 3 input wavenumber IPEROUT 3 output wavenumber MONITR 0 NUMHDR 1 NOOUT 111101111 PANEL SIZE 18 ILOG 1 NPDIPOLE 2 4 6 Input file test21 pot TEST21 POT SPAR with three strakes igdef 12 TEST21 GDF oe 1 1 IRAD IDIFF 3 NPER array PER follows 0 1 0 5 1 2 NBETA array BETA follows 0 120 1 NBODY test21 gdf 0 0 0 0 XBODY 1 1 1 1 1 1 IMODE 1 6 Input file test21 gdf TEST21 SPAR2 with three strakes IGDEF 12 18 9 80665 ULEN GRAV 0 0 ISX ISY 7 12 NPATCH IGDEF 5 18 200 RADIUS DRAFT Bilis S WIDTH THICKNESS TWIST NSTRAKE 0 IRRFRQ O IMOONPOOL RADIUSMP 0 0 IMPGEN Input file test21 frc TEST21 FRC
113. 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 imass mass matrix of body 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 idamp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O istif 0 oO 0000000 oO OOOO O CO oO Oo0Oo000000O OM OD OO So ooo O28 0 0 OG O 00 00000 O 0 000000 O 0000000 Input file testi7c cfg ILOWHI 1 IALTFRC 1 ISOLVE 1 PANEL SIZE 0 2 use default spl parameters IPERIN 3 input wavenumber IPEROUT 3 output wavenumber IRR 0 ILOG 1 NUMHDR 1 NPFSP 4 4 free surface pressure on patch 4 IMODESFSP 1 use NEWMODES subroutine PRESSURE_FS NMODESFSP 1 1 pressure mode same symmetry as heave Input file testi7c pot TEST17c cylinder with free surface pressure in moonpool 0 1 IRAD IDIFF 61 0 100000 0 150000 0 200000 0 250000 0 300000 0 350000 0 400000 0 450000 0 500000 0 550000 0 600000 0 610000 0 620000 0 630000 0 640000 0 650000 0 660000 0 670000 0 680000 0 690000 0 700000 0 710000 0 720000 0 730000 0 740000 0 750000 0 760000 0 770000 0 780000 0 790000 0 800000 0 810000 0 820000 0 830000 0 840000 0 850000 0 860000 0 870000 0 880000 0 890000 0 900000 0 910000 0 920000 0 930000 0 940000
114. 1 1 1 1 3 3 0 2 2 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 50 O 1 5 0 0 5 end of file A 12 IRREGULAR FREQUENCY REMOVAL TEST12 TEST12 is the higher order analog of TESTO2 intended to illustrate the removal of irregular frequency effects using the higher order method As in TEST 11a the geometry is defined analytically IGDEF 1 and the dimensions are input in the file TEST12 GDF In this case NPATCH 3 is specified where the additional patch corresponds to the inte rior free surface as required for the irregular frequency option In the figures below the patch and panels on the interior free surface are shaded red One quadrant of the side and interior free surface are omitted to show the bottom surface Input file testi2 cfg TEST12 CFG Cylinder R 1 T 0 5 igdef 1 npatch 3 IRR 1 ILOWHI 1 IRR 1 ILOG 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 Input file test12 pot TEST12 POT Cylinder R 1 T 0 5 igdef 1 npatch 3 IRR 1 a 1 1 IRAD IDIFF 3 NPER array PER follows 8 971402 2 006403 1 003033 2 NBETA array BETA follows 0 45 1 NBODY test12 gdf 0 0 0 0 XBODY 11 1 1 1 1 IMODE 1 6 Input file testi2 gdf TEST12 cylinder R 1 T 0 5 analytic geometry npatch 3 1 9 80665 ULEN GRAV 1 1 ISX ISY 3 1 NPATCH IGDEF 2 NLINES 1 0 0 5 RADIUS DRAFT 0 UNIFORM MAPPI
115. 11 The control surfaces surrounding the cylinder and spheroid are defined by the input files TEST13c csf and TEST13s csf These control surfaces are generated by the subroutines CIRCYL_CS and ELLIPSOID CS in the GE OMXACT DLL library The surfaces generated by these subroutines include the portion of the free surface between the body and outer control surface The corresponding output for the mean drift force and moment is contained in the file TEST13 9c Input file testi3 cfg TEST13 CFG Cylinder spheroid ILOWHI 1 IPLTDAT 4 ILOWHI 1 IRR 0 ISOLVE 2 KSPLIN 3 IQUADO 3 IQUADI 4 NUMHDR 1 NOOUT 0 1 IALTFRC IALTFRCN 110 3 11 1111 Input file testi3 pot Alternative Form 3 FRC TEST13 POT Cylinder spheroid ILOWHI 1 lt 1 1 1 PER testi3c gdf 1 25 0 0 0 0 0 0 1 1 1 1 1 1 test13s gdf 0 5 0 0 0 0 90 0 1 1 14 1 1 1 Input file testi3c gdf TEST13C cylinder R 1 T 2 1 9 80665 ULEN GRAV 1 1 ISX ISY NPATCH IGDEF NLINES RADIUS DRAFT UNIFORM MAPPING 0 2 0 ee NN Input file test13c spl TEST13C cylinder R 1 T 2 8 8 NU NV side 8 4 NU NV bottom IRAD IDIFF NPER array PER follows NBETA array BETA follows BETA NBODY XBODY IMODE 1 6 XBODY IMODE 1 6 analytic geometry npatch 2 analytic geometry npatch 2 Input file testi3s gdf TEST13S spheroid a 2 b c 0 25 igdef 4 1 9 80665 ULEN GRAV 1 1 ISX ISY 1 4 NPATCH IGDEF 1 NLINES 2 0 0 25 0 2
116. 2 tank2 bot aft top fwd side bot 2 000000 2 100000 1 100000 2 000000 2 100000 0 000000 2 000000 0 000000 0 000000 patchi6 tank2 aft 2 000000 2 100000 0 000000 0 000000 2 100000 0 000000 0 000000 0 000000 0 000000 2 000000 0 000000 0 000000 patchi7 tank2 top Input file test22b spl TEST22b SPL FPSO with two tanks rigid tops 4 3 CCO CO OCO O OO O wN O O WNHWNHNWNHWNHNNWEHEN W DH Input file test22b frc test22b frc fpso with 2 tanks xbody3 1 2 1 1 1 1 0 0 14 1 1 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 0 NFIELD A 23 RADIATED WAVE FIELD FROM A BANK OF WAVE MAKERS TEST23 Several variants are considered to illustrate the analysis of wavemakers in a wave tank In TEST 23 following the procedure in Section 12 3 the option ISOLVE 1 is used to compute the radiated waves from a bank of paddle wavemakers The wavemakers are in the plane x 0 of a rectangular tank as shown below The tank has a reflecting wall at y 0 The tank depth is 4m Each wavemaker is represented by one rectangular patch using IGDEF 0 with the vertices listed in TEST23 GDF The motion of each wavemaker is rotational about its lower edge at the same depth below the free surface represented by a generalized mode with the same distribution of normal velocity and with symmetry prescribed about the walls x 0 and y 0 These generalized modes
117. 2 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 Input file testila pot TEST11A POT Cylinder R 1 T 0 5 igdef 1 a 1 1 IRAD IDIFF 2 NPER array PER follows 8 971402 2 006403 1 NBETA array BETA follows O 1 NBODY testila gdf 0 0 0 0 XBODY 11 1 1 1 1 IMODE 1 6 Input file testila gdf TESTila cylinder R 1 T 0 5 analytic geometry npatch 2 1 9 80665 ULEN GRAV 1 1 ISX ISY 2 1 NPATCH IGDEF 2 1 0 0 5 RADIUS DRAFT 0 UNIFORM MAPPING Input file testila spl TESTila spl cylinder R 1 T 0 5 analytic geometry npatch 2 4 2 NU NV Patch 1 side u azimuthal v vertical 4 2 NU NV Parch 2 bottom u azimuthal v radial Input file testila frc TEST11a FRC Cylinder R 1 T 0 5 igdef 1 1 1 1 1 3 3 0 2 2 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 50 O 1 5 0 0 5 end of file Input file TEST11b CF ILOWHI 1 IRR 0 ISOLVE 2 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 1 1 Input file TEST11B POT mils testilb cfg G Cylinder R 1 T 0 5 igdef 1 1101111 testilb pot Cylinder R 1 T 0 5 igdef 1 1 1 IRAD IDIFF 2 NPER array PER follows 8 971402 2 006403 2 NBETA array BETA follows 0 45 1 NBODY testilib gdf 0 0 0 0 XBODY 1 1 1 1 1 1 IMODE 1 6 Input file test11b gdf TEST11 cylinder R 1 T 0 5 analytic geometry nonuniform mapping 1 9 80665 ULEN G
118. 2 the input file directory_wam txt should be made with a listing of all fnames files to be processed This can either be done manually by the user or automatically using the batch file V6V7 bat which also runs the program If the batch file is saved with V6V7inp exe in a directory identified by the system PATH it can be executed from each directory containing old input files simply by typing the command V6V7 This automatically performs the steps 1 and 2 above and then runs the program Alternatively these three steps can be performed manually by the user The simplest way to make the input file directory wam txt manually is to execute the DOS command dir wam gt directory_wam txt which produces a DOS directory list of all fnames files The program ignores extraneous columns in this directory and only uses the character string containing wam if this is found When the program is run a list of the fnames files is output to the monitor with a list of modified input files appended The same list is saved in the file v6v7inp log Input files which are modified are saved in the sub directory V7inp If the user wishes to update the input files for each run simply execute the DOS command copy v7inp to overwrite the original files in the directory with the new files Before overwriting with the new files it may be advisable to save the old input files for example by copying them to a sub directory V6inp Special situations which shou
119. 2177 4430902 9789203 16487078 O 0 O O O 0 824354 9789203 37899671 64382041 0 0 O O O O 1339575 16487078 64382041 162406554 A 9 SPAR WITH THREE STRAKES TESTO9 This test run analyzes a circular cylinder with three spiral strakes The strakes are modeled as zero thickness dipole panels following the method described in Section 5 4 The radius of the cylinder is 18m and the draft is 200m The strake width is 3 7m There are no planes of symmetry due to the twist of the strakes A total of 960 panels are used including 672 on the cylinder plus 288 on the strakes The excerpts from the GDF file include the first body panel and also the first dipole panel In TESTO9A the trimmed waterline option is used with the parameters ITRIMWL and XTRIM specified in the file TESTO9A CFG These parameters specify a vertical trim of 10m and a pitch angle of 10 degrees The same TEST09 GDF file is used for both tests Only the filenames are changed in TESTO9A POT and TESTO9A FRC Perspective views in the untrimmed and trimmed conditions are shown below The FORCE run includes all options which can be evaluated without using the source formulation ISOR 1 since the latter option cannot be used with dipole panels The body pressure file TESTO9 5p includes the pressure on the body panels and the pressure jump on the dipole panels The corresponding panel centroids are listed in the output file TEST09 PNL The figure below shows the submerge
120. 3 7 3 8 3 9 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 WAMIT Version 7 Changes introduced in Version 7 0 Changes introduced in Version 7 1 GETTING STARTED Installation and setup Demonstration programs Standard test runs Running Test 01 Running Test 11 Other test runs Using multiple processors Memory and storage restrictions Modifying the input files DEFINITION OF QUANTITIES EVALUATED BY WAMIT Hydrostatic data Added mass and damping coefficients Exciting forces Body motions in waves Hydrodynamic pressure Free surface elevation Velocity vector on the body and in the fluid domain Mean drift force and moment Zero and infinite wave periods INPUT FILES Summary of changes in Version 7 input files The Potential Control File The Force Control File Alternative form 1 The Force Control File Alternative form 2 Definition of fixed or free modes Body pressure and fluid velocity at specified points Configuration files CONFIG WAM and CFG Filenames list FNAMES WAM File names File format Uniform arrays of field points Using the optional file BREAK WAM Assigning RAO S in an external file Evaluating FORCE outputs in POTEN IFORCE 2 5 lon oo No E it 8 4 enn in he co Barana files 8 5 Global symmetry indices 8 6 Output GENERALIZED BODY MODES NEWMDS gt 0 9 1 Input Files 9 2 Using DEFMOD with the Low 5 1 The formatted output file out 5 2 Numeric
121. 5 A B C Input file testi3s spl TEST13S spheroid A 2 B C 25 analytic geometry npatch 1 8 4 NU NV Input file testi3 frc TEST13 FRC Cylinder spheroid ILOWHI 1 1 1 1 1 1 3 1 1 1 1 0 test0bc frc test05s fre 0 1 0 0 0 Input file testi3c csf testi3c csf cylinder control surface 1 ILOWHICSF 11 ISX ISY 3 1001 1 NPATCH ICDEF PSZCSF 2 1 2 2 2 1 RADIUS DRAFT Inner radius 0 uniform mapping Input file testi3s csf ELLIPSOID CONTROL SURFACE defined by subroutine ELLIPSOID _CS 1 ILOWHICSF IRERE i ISX ISY 2 1003 1 0 NPATCH IGDEF PSZCSF 2 NLINES 2 20 3 0 3 A B C semi axes of outer control surface 2 0 0 25 semi axes of body waterline TEST13A illustrates the use of trimmed waterlines as specified by the last three lines of the file TEST13A CFG The cylinder is raised vertically by Im and rotated about the pitch axis by 15 degrees The options IRR 3 and IRR 1 are used to remove irregular frequency effects as described in Section 9 4 The interior free surface of the spheroid is defined by the GDF file and subroutine ELLIPSOID with IRR 1 See Sections 6 8 and 9 1 The interior free surface of the trimmed cylinder is defined automatically by the program based on the trimmed waterline with IRR 3 See Section 9 4 Since the cylinder is trimmed the waterplane is elliptical and the IRR 1 extension of CIRCCYL in GEOMXACT is not valid Note that NPATCH 2 is assigned in testl3as gdf to provide for the i
122. 5 AUTOMATIC CONTROL SURFACES For bodies with regular waterlines it is possible to define the control surface automatically during the run The higher order option ILOWHICSF 1 must be specified for the control surface but either the low order ILOWHI 0 or higher order ILOWHI 1 options can be used for the body geometry and solution When this procedure is used the outer part of the control surface is defined either as a circular cylinder of specified radius and depth or by a quadrilateral box usually rectangular with specified waterline vertices and depth The program automatically defines the intermediate free surface between the outer boundary and the body waterline s by first tracing the waterlines and then establishing appropriate patches to cover the area of the free surface between the waterlines and the outer boundary This procedure can be used with multiple waterlines as in the case of a TLP semi sub or catamaran In these cases it is necessary to define quadrilateral partitions which separate the waterlines and serve to define the outer boundaries of local patches surrounding each waterline Examples of these inputs are shown below for the TLP and semi sub When partitions are used for this purpose certain restrictions must be followed e The patches defined by the partitions and the waterline of the outer control surface must cover the free surface with no gaps or overlaps e Each partition as well as the outer wat
123. 9 can be combined in the form Lge Tg OnSw Sp 15 72 where L 0 0 o Sv n K on Sp 15 73 When necessary and Le will be used to indicate that the normal derivative is with respect to the corresponding coordinates The integral equation 15 11 for the velocity potential is replaced by pi ff OCC de ff nale 15 74 The factor 27 is applied if the boundary surface is below z 0 and 4r is applied if the boundary surface is on z 0 In the latter case the integral over S on the left hand side of 15 74 vanishes since the Green function satisfies the homogeneous free surface condition In the source formulation where the potential is given by 15 24 the integral equation corresponding to 15 26 is a aj x fff ELGE E f nalea 15 75 In the diffraction problem the potential 15 8 satisfies the integral equation 27 i eo ff eol Cec xg amoo 15 76 b The definitions of the added mass and damping coefficients in the first equation of Sec tion 3 2 are unchanged except for the extended range of the subscripts i j In the defini tion of the Haskind exciting forces in Section 4 3 the normal derivative of the incident wave potential is replaced by Lyo The definition of the exciting forces from direct integration of pressure is given by the second equation in Section 3 3 without change The definitions of the hydrostatic restoring coefficients C for i j lt 6 are unchanged as given in
124. A The coordinates of field points XFIELD where the pressure wave elevation and velocity are evaluated are defined as in Section 4 3 relative to the wall mounted system The incident wave velocity potential is defined relative to the wall mounted coordinate system Consequently the phases of the exciting forces motions hydrodynamic pressure and field velocity induced by the incident wave are understood relative to the incident wave elevation at X Y 0 In addition the fluid velocity vector components are given with respect to the wall mounted coordinate system The other definitions of output quantities in Chapter 3 are unchanged Wavemakers may be included in the walls following a similar procedure as described in Section 12 3 When bodies and wavemakers are both present ISOLVE gt 0 must be spec ified The wavemakers are treated as one or more separate bodies In the simplest case where one body is in the fluid domain and all wavemakers are defined within another GDF file NBODY 2 is used and the parameter IBODY W 2 is defined in the CFG file indicat ing that body 2 consists of wavemakers in the walls The order of the bodies is specified by the order of the corresponding inputs in the POT file There can be one or more physical bodies and one or more wavemaker bodies The physical bodies must precede the wave maker bodies in all cases Thus if K 1 2 NBDYP are the indices for NBDYP physical bodies and K NBDYP 1 NBDYP 2 NBDYP
125. Appendix illustrate this application For a single body with no generalized modes NDFR 6 in all cases For the analysis of multiple bodies cf Chapter 8 with no generalized modes NDFR 6 NBODY If generalized modes are analyzed cf Chapter 9 NDFR is the total number of modes for all bodies including both rigid body modes and generalized modes Thus in the most general case NDFR 6 NBODY 53 NB DY NEWMDS n If fixed free modes are specified for multiple bodies using IALTFRC 3 as described in Section 8 3 the modifications 1 and 2 described above must be included only in the Global Force Control File GFRC and not in the separate Force Control Files for each body It is also possible to perform the analysis in FORCE for a problem where no incident waves exist after running POTEN with incident waves present and with the diffraction solution obtained To suppress the incident waves in FORCE IOPTN 4 3 is assigned in the FRC file In that case the body pressure velocity field point pressure velocity and mean drift forces are evaluated assuming that the body is oscillating in the specified free mode s without incident waves 4 6 BODY PRESSURE AND FLUID VELOCITY AT SPECI FIED POINTS If IOPTN 5 gt 0 the points on the body surface where the pressure and fluid velocity are evaluated depend on the parameter IPNLBPT in the configuration file In the default case IPNLBPT 0 these points are at the panel centroids in the low order m
126. BPO file should be checked to verify that the correct patch is used especially in cases where there is ambiguity between the pressure on a conventional patch and the pressure jump on a dipole patch Similarly in the low order method the panel indices N1 N2 in the BPO file can be checked to verify the corresponding output at the points in BPI files is the pressure obtained from those on the conventional body panels or the pressure jump on the dipole panels 4 7 CONFIGURATION FILES CONFIG WAM AND x CFG Two optional configuration files may be used to specify various parameters and options in WAMIT The first configuration file is assigned the reserved name config wam The second filename is specified by the user with the extension cfg Both files are opened and read if they exist and the configuration parameters defined below can be included in either the first or second file It is recommended to use the first file for parameters which are the same for most or all applications and to use the second file for parameters which depend on the specific run If the same parameter is defined in both files the input from the second is used for the run If the second configuration file is used its complete filename including the extension cfg must be included in the input file fnames wam The test runs listed in Appendix A show examples of these conventions The inputs which may be specified in the configuration files are as
127. CH NVG NPATCH KUG NPATCH KVG NPATCH VKNTUG 1 NPATCH VKNTUG NUA NPATCH NPATCH VKNTVG 1 NPATCH VKNTVG NVA NPATCH NPATCH XCOEF 1 1 XCOEF 2 1 XCOEF 3 1 XCOEF 1 2 XCOEF 2 2 XCOEF 3 2 XCOEF 1 NB NPATCH XCOEF 2 NB NPATCH XCOEF 3 NB NPATCH Here IGDEF 1 is assigned on line 4 to specify the B spline representation of the geometry NUG I and NVG I are the numbers of panel subdivisions of the u and v coordinates on I th patch KUG I and KVG I are the orders of B splines VKNTUG J D is the B spline knot vector in u on patch I J 1 2 NUA I NUA I NUG I 2 KUG D 1 VKNTVG J I is the B spline knot vector in v on patch I J 1 2 NVA I NVA I NVG 1 2 KVG I 1 XCOEF 1 K XCOEF 2 K XCOEF 3 K are the components of the vector co efficient X in 7 6 These are defined in terms of the single array index K where K 1 2 NB I Here NB I is the total number of coefficients on patch I given by the relation NB I NUG I KUG I 1 x NVG I KVG I 1 TEST11 Appendix Section A 11 is an example of this type of GDF input file 7 7 GEOMETRY REPRESENTED BY MULTISURF IGDEF 2 WAMIT includes the option to import ms2 geometry database files from the CAD program MultiSurf directly into WAMIT and to represent the geometry during execution of WAMIT by linking to the MultiSurf kernel A detailed description of this option is contained in Reference 24 The principal advantages of this option are a the repres
128. CH FILES Two types of temporary scratch files are opened during execution of the subprogram POTEN One group are opened formally using the FORTRAN scratch file convention with filenames which are assigned by the compiler The second group are opened with the temporary filenames SCRATCHA SCRATCHB SCRATCHO All of these files are deleted prior to the end of the run but if execution is interrupted by the user or by power interruption to the system some or all of these scratch files may remain on the hard disk In the latter case the user is advised to delete these files manually If the storage requirements of a run exceed the available disk space a system error will be encountered in this event the user should either increase the available disk space or reduce the number of panels or solutions The parameter SCRATCH_PATH can be used in the configuration files to distribute storage between two disks as explained in Section AT 14 6 MULTIPLE PROCESSORS NCPU gt 1 WAMIT Version 7 0pc is compiled with the Intel Fortran Compiler Version 12 using special directives to enable parallel processing on systems with multiple processors Depending on the inputs and hardware the total run time can be reduced substantially by using this capability Figure 14 2 shows two examples using modified inputs of the test runs 07 ISSC TLP and 15 Semi sub which are described in Appendix A and using the low order and higher order options respectively In
129. CSF X1 1 Y1 1 Z1 1 X2 1 Y2 1 Z2 1 X3 1 Y3 1 Z3 1 X4 1 Y4 1 Z4 1 X1 2 Y1 2 Z1 2 X2 2 Y2 2 Z2 2 X3 2 Y3 2 Z3 2 X4 2 Y4 2 Z4 2 X4 NPANCSF Y4 NPANCSF Z4 NPANCSF header denotes a one line ASCII header dimensioned CHARACTER 72 ISXCSF ISYCSF are the geometry symmetry indices which have integer values 0 or 1 If ISXCSF and or ISYCSF 1 x 0 and or y 0 is a geometric plane of symmetry and 11 4 the input data are restricted to one quadrant or one half of the control surface Conversely if ISXCSF 0 and ISYCSF 0 the complete control surface must be represented by panels ISXCSF 1 The x 0 plane is a geometric plane of symmetry ISXCSF 0 The z 0 plane is not a geometric plane of symmetry ISYCSF 1 The y 0 plane is a geometric plane of symmetry ISYCSF 0 The y 0 plane is not a geometric plane of symmetry For all values of ISXCSF and ISYCSF the x y axes are understood to belong to the body system of the corresponding GDF file and the panel data are always referenced with respect to this system NPANCSF is equal to the number of panels with coordinates defined in this file XI J YI J ZI J are the Cartesian coordinates x y z of I th vertex of the J th panel The four vertices of a panel are specified in the anti clockwise direction when the panel is viewed from outside of the control surface as in the case of the body surface illustrated in Figure 6 1 11 3 HIGHER ORDER CO
130. D WAVEMAKERS WITH VERTICAL WALLS WAMIT includes the option to account for images of the body in the presence of one vertical wall or two vertical walls which intersect at a right angle The presence of walls is specified by the optional integer inputs IWALLXO and IWALLYO in the configuration files In the default case these inputs are assigned the values zero signifying that there are no walls The inputs IWALLX0 1 and or IWALLY0 1 signify that there are walls in the planes x 0 and or y 0 respectively All other inputs are unchanged from the case without walls In particular the GDF files for one or more bodies should specify the symmetry indices ISX ISY corresponding to the planes of symmetry of the body with values O or 1 just as in the case without walls Figure 12 1 defines two coordinate systems one fixed on the body and the other on the wall The axes of the former are denoted by x y z and those of the latter by X Y Z In the presence of wall s the global coordinate system defined in Section 4 2 must coincide with the wall coordinate system as defined in Figure 12 1 XBODY 1 Figure 12 1 Definition sketch of coordinates In the Potential Control File the vector XBODY 1 X BODY 2 X BODY 3 speci fies the dimensional X Y Z coordinates of the origin of the body fixed coordinate system relative to wall system in the units of the length ULEN XBODY 4 is the angle in de grees formed by the body x axis and the X
131. D and defining conventional circular cylindrical coordinates r 0 z appropriate choices for the parametric coordinates are 40 r oS ee 9 7 1 on the bottom where 0 lt 6 lt 7 2 and 0 lt r lt R and 40 z Ie za w 7 2 w i y 2 7 2 on the side where 0 lt 6 lt 7 2 and D lt z lt 0 In order to give a consistent definition for the normal vector we impose the right hand convention if the fingers of the right hand are directed from u toward v the thumb should point out of the fluid domain and into the interior domain of the body With these definitions the Cartesian coordinates x y z of any point on either patch can be expressed in terms of the parametric coordinates u v More generally any physically relevant body surface can be represented by an ensemble of appropriate patches where the Cartesian coordinates of the points on each patch are defined by the mapping functions xz X u v y Y u v z Z u v 7 3 This is the fundamental manner in which the body surface is represented for the higher order option of WAMIT Alternative methods for prescribing these mapping functions are described separately in Sections 7 5 7 8 In order to provide a systematic procedure for refining the accuracy of approximations on each patch a set of smaller surface elements are defined as described in Section 7 2 For this purpose each patch is sub divided in a rectangular mesh in parametric space These elements are referre
132. DRAFT NCYL XC NCYL YC NCYL The last column indicates the dimensions and other input parameters to be included in the GDF file Where two or more lines of inputs are shown in the table the GDF file should follow the same format as illustrated in the test runs Brief descriptions of each subroutine are given below More specific information is included in the comments of each subroutine These bodies can be combined for multiple body analysis as described in Chapter 8 without modifications of the subroutines 7 17 CIRCCYL defines a circular cylinder as explained above ELLIPCYL defines an elliptical cylinder with semi axes A B If A B RADIUS the re sults are identical to using CIRCCYL The options NPATCH 1 bottom mounted and NPATCH 3 IRR 1 are the same as for CIRCCYL The semi axes A and B coincide with the x and y axis of the body coordinate system respectively SPHERE defines a floating hemisphere with one patch on the body surface If NPATCH 2 the interior free surface is included for use with the irregular frequency option IRR 1 The optional parameter INONUMAP can be included to specify either uniform INON UMAP 0 or nonuniform INONUMAP 1 mapping Uniform mapping is the default and it is not necessary to include INONUMAP in this case If INONUMAP 1 is specified the mapping in the azimuthal direction on the hemisphere is quadratic to give a finer dis cretization close to the waterline Similarly if IRR 1 IN
133. During operation of the WAMIT RGKernel interface a log file is opened and written to in the working folder the same folder that contains the GDF file This file named RGKLOG TXT contains an echo of XBODY and GDF data a reflection of some information extracted from the M S2 model file s brief reports on some aspects of interface initialization and utilization and possible warning and error messages RGKLOG TXT also includes a summary tabulation of surfaces vs global body and patch indices which will give the correct order of surfaces for constructing an SPL file if desired Example RGKLOG TXT log file for RG2WAMI T DLL tarting procedure BODY 1 RGKI NIT at 25 Nov 2001 13 59 49 Data for body no DY 0 000 ncated cylinder 1 000 1 length TSY q PATCH 2 IGDEF E G unit GRAV de 0 000 0 000 0 000 example 1 0 m radius 9 80660 deduced from GRAV 0 5 m draft is m 2 MS2 filename TRCY Entity List of wet Model will be eval Unit normals are o Opened Body 1 Body 1 tch 1 sur tch 2 sur pal pal RG model fil L2 MS2 ted surfaces wetted surfs uated in FAST mode utward e TRCYL2 MS2 face name side surf face name bottom surf index 1 2 body igdef 1 2 2 surface name side surf bottom surf patch 1 2 ior Exiting RGKINIT at 25 Nov 2001
134. ERNAL FORCES mmx The file frc hst is created to output values of the nondimensional hydrostatic matrix C in the following format I J I J This matrix is defined in Section 3 1 The file frc mmx is created to output the dimensional values of the external mass damping and stiffness matrices and other data The format and data included in this file depend on the parameters NBODY NMODES and IALTFRC An abbreviated copy of this file for the standard test run TESTOS described in Section A 8 is shown below WAMIT Force Output File test08 mmx 14 Apr 2013 18 08 59 Gravity 9 80665 Length scale 1 00000 NBODY 1 IALTFRC 2 WAMIT Ouputs for body N 1 IALTFRCN 2 Volumes VOLX VOLY VOLZ 62731 0 62731 0 0 308443E 01 Center of Buoyancy Xb Yb Zb 0 000000 0 000000 0 000031 Center of Gravity Xg Yg Zg 0 000000 0 000000 1 000000 External force matrices I J MASS I J DAMP I C STIF I J 1 1 0 000000E 00 0 000000E 00 0 000000E 00 1 2 0 000000E 00 0 000000E 00 0 000000E 00 1 3 0 000000E 00 0 000000E 00 0 000000E 00 5 9 10 8 6 283200E 04 0 000000E 00 1 648708E 07 10 9 6 283200E 04 0 000000E 00 6 438204E 07 10 10 6 568800E 04 0 000000E 00 1 624066E 08 The external force matrices are defined in Sections 4 4 and 8 2 If IALTFRC 1 is used to input the body inertia from the products of inertia as explained in Section 4 3 the equivalent mass matrix is output in the mmx file normalized by the fluid density If NB
135. F 1 E 1 E E FO 509 f ical pk Eta x dl Seok Fangs em canja a6 1 p ff WoR vo Vos E pk ff E Ay Vo ds FO 15 58 MO zes Z x n dl pg Sl E ax W x kd f i Ex BE G ony aan al 1 o ff lex vase 3E x AV Voas a pf ex 5 Vo V ds MY 15 59 IALTCSF 2 FO og f REA J as PF fa ci amp x 7 nl Nz no 2 sgh we 3 ary a2x dl off wore SVO V jlas ok ff Em Lyg Vo ds FO 15 60 15 14 1 2 gt 272 gt M 509 f bb x HG a pg Ex V s WL 500 fyr Fee PE my aan o 1 off Ex VOZ 3E x m V6 Vo lds eff E x Ryo Se 5V Vo ds MP 15 61 In these equations Se is the submerged part of the control surface S is the part of the control surface on the free surface W L is the body waterline and CL is the common boundary of Sc and Sy 7 denotes the two dimensional normal vector in the horizontal plane on the body waterline pointing into the body V is the gradient in the horizontal plane and k is the unit vector pointing vertically upward F 2 and M 2 are the hydrostatic components 15 56 15 57 The derivations of the equations 15 58 15 61 from 15 54 15 55 are given in Reference 28 15 10 INTERNAL TANK EFFECTS The solution for the velocity potential in each tank and the resulting forces and moments are computed in a similar manner as for the exterior domain outside the body or bodies
136. Haskind wave headings in degrees The Haskind wave headings may be introduced in the Force Control File as an option to enable evaluations to be made of the Haskind exciting forces Option 2 and body motions in waves Option 4 at heading angles not included in the Potential Control File This option is feasible since the evaluation of Haskind exciting forces requires only the radiation potentials already determined by POTEN This is a useful feature when the computational time is significant since the time required to solve many diffraction problems in POTEN greatly exceeds the time required to evaluate the Haskind exciting forces in FORCE Since the number of Haskind wave headings will affect the subsequent READ statements for data in the Force Control File it is important to ensure that this number corresponds with the prescribed integer NBETAH In particular if NBETAH 0 no values of BETAH should be included and NFIELD should appear on the next line of the Force Control File If NBETAH gt 0 is specified the settings of the IOPTN switches are automatically set equal to 0 for options 3 5 6 7 8 NFIELD is the number of points in the fluid domain free surface where the hydrody namic pressure wave elevation and or velocity are to be evaluated NFIELD must be an integer greater than or equal to zero XFIELD is a three dimensional array with dimensions 3 x NFIELD defining the dimen sional global coordinates of field points where the pressure
137. IDTH and THICKNESS are the width and thickness of the strakes Helical form of strakes can be generated by specifying nonzero TWIST which represents the number of revolutions from top to bottom in the counter clockwise direction viewed from the top IRRFRQ 1 includes the interior free surface and in this case IRR 1 should be specified in the configuration file IRRFRQ 0 indicates no interior free suface patch The spar may have a uniform circular moonpool at the center IMOONPOOL 1 includes a moonpool and IMOONPOOL 0 does not RADIUSMP is the radius of the moonpool IMPGEN 1 includes the moonpool free surface to specify the generalized modes on that surface Otherwise set IMPGEN 0 AUV defines one quadrant of an axisymmetric submerged body with vertical axis The body is defined by a hemispherical bow of radius RADIUS conical tail of length DTAIL and optional cylindrical midbody of length DCYL The origin is at the center of the cylindrical midbody If NPATCH 2 and DCYL 0 0 the midbody is omitted SPAR2 defines the first quadrant of a circular cylinder of radius RAD1 with a circular damping skirt of radius RAD2 on the lower part of the cylinder The lower surface of the skirt is in the plane of the bottom of the cylinder at Z DRAFT and SKIRT_HEIGHT is the height of the skirt NPATCH 4 is the conventional case NPATCH 5 includes the interior free surface for use with IRR 1 and NPATCH 3 can be used for a bottom mounted structure SPHERXYZ
138. IELD ARRAYS is an integer parameter specifying if uniform arrays of field points are assigned in the FRC control file using a compressed format as explained in Section 4 11 IFIELD_ARRAYS 0 Field point data is assigned only as shown in the conventional FRC files as explained in Sections 4 3 and 4 4 IFIELD_ARRAYS 1 Additional field point data is assigned in the conventional FRC files as explained in Section 4 11 The default value is IFIELD ARRAYS 0 IFORCE is an integer parameter specifying if the FORCE subprogram is executed during the WAMIT run IFORCE 0 Do not execute FORCE IFORCE 1 Execute FORCE IFORCE 2 Execute FORCE and POTEN simultaneously for each wave period see Section 4 14 The default value is IFORCE 1 IGENMDS is an integer parameter specifying the option to input the geomeric data associated with the mode shapes of generalized modes when NEWMDS gt 0 The details on the use of the generalized mode option are described in Chapter 9 IGENMDS 0 use a seperate program DEFMOD to input the geometric data for gen eralized modes This option can be used only with the low order method ILOWHI 0 In this case the user prepares a subroutine in DEFINE to describe the generalized mode shapes IGENMDS 0 use a DLL file containing the subroutine NEWMODES The user modifies NEWMODES to specify the mode shape This option can be used with both the low and higher order options The default value is IGENMDS 0
139. IGDEF 2 The barge has a length of 100m beam 20m and draft 4 8m with one plane of symmetry y 0 The origin of the body coordinate system is at the intersection of the waterplane and midship section The format of the GDF file is as explained in Section 6 7 and Ap pendix 2 Four patches are used on one side of the body to represent the forebody parallel middlebody afterbody and transom Reference 24 includes results for a multiple body configuration including two barge hulls identical to this model The body pressure is evaluated at the points specified in the input file test20 bpi as explained in Section 4 11 The parameter IPNLBPT 1 in the cfg file is used to specify this option with the input points specified in the body coordinate system Input file test20 cfg TEST20 CFG MultiSurf barge ipltdat 4 ILOWHI 1 IALTFRC 1 ISOLVE 1 NUMHDR 1 panel_size 10 IPNLBPT 1 Input file test20 pot single barge based on MultiSurf model igdef 2 1 1 IRAD IDIFF 3 NPER array PER follows 6 9 12 3 NBETA array BETA follows 180 135 90 1 NBODY test20 gdf 0 0 0 0 0 0 0 0 XBODY ie do di ad IMODE 1 6 Input file test20 gdf Test run for barge modelled with MultiSurf 1 000000 9 80665 ULEN GRAV O 1 ISX ISY O 2 NPATCH IGDEF 3 NLINES test20 ms2 wetted_surfs O O O FAST DivMult outward normals Input file test20 frc test20 frc igdef 2 1 1 1 1 1 O O 11 IOPTN 1 9 0 0 VCG 10 00000 0000000 0000000 00
140. IPEROUT 3 output wavenumber ILOG 1 NUMHDR 1 IGENMDS 17 NEWMDS 2 Input file testifa pot TEST17 cylinder with moonpool NPATCH 3 gs E 0 0 IRAD IDIFF NPERGROUP 3 11 0 10 0 05 end of group 1 K 0 10 to 0 60 40 0 61 0 01 end of group 2 K 0 61 to 1 00 10 1 05 0 05 end of group 3 K 1 05 to 1 50 1 NBETA array BETA follows 180 1 NBODY test17a gdf 0 0 0 0 XBODY 1 O 1 O 1 0 IMODE 1 6 Input file testi7a gdf TEST17a cylinder with moonpool undamped patch on free surface 1 9 80665 ULEN GRAV 1 1 ISX ISY 4 7 NPATCH IGDEF 1 NLINES 0 5 1 0 0 25 radius draft moonpool radius Input file test17a frc TEST17a moonpool with generalized modes for free surface no damping 1 1 1 1 0 0 0 0 o0oo0oo0o0o0o0o0O Le 0 0 0 1 imass mass matrix of body 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 589 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 147 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O idamp O istif 0 Input file testi7b cfg TEST17B CFG file cylinder with moonpool damped lid ILOWHI 1 IPOTEN 0 IALTFRC 2 ISOLVE 1 PANEL SIZE 0 2 use default spl parameters IPERIN 3 input wavenumber IPEROUT 3 output wavenumber ILOG 1 NUMHDR 1 IGENMDS 17 NEWMDS 2 Input file testi7b frc TEST17b cylinder moonpool generalized modes damping b33 4 b77
141. ISOLVE NEQN in this case the result is identical to using the iterative solver without blocks ISOLVE 0 The iterative method is useful primarily for the low order method where NEQN is relatively large and the rate of convergence is good in most cases Usually in the low order method the number of iterations required to obtain convergence is in the range 10 20 In the standard test runs described in Appendicies A using the low order method the iterative or block iterative solvers converge within the default number of iterations MAXITT 35 for all cases except TESTO2 Experience using the low order method has shown that slow convergence is infrequent and limited generally to special applications where there either is a hydrodynamic resonance in the fluid domain as in the gap between two adjacent barges or in the non physical domain exterior to the fluid volume An example of the latter is a barge of very shallow draft where the irregular frequencies are associated with non physical modes of resonant 14 4 wave motion inside the barge These types of problems can often be overcome by modifying the arrangement of the panels or increasing the number of panels For the higher order method the linear system loses diagonal dominance as the order of the basis functions increases as shown in the expression for d in 15 32 Experience indicates that the convergence rate is reduced and it is generally advisable to use the direct solver ISOLVE 1
142. IT Cartesian coordinates are used to define the body geometry forces and other hydrody namic quantities evaluated by WAMIT These are output in nondimensional forms in terms of the appropriate combinations of the water density p the acceleration of gravity g the incident wave amplitude A frequency w and the length scale L defined by the input parameter ULEN in the GDF file The notation and definitions of physical quantities here correspond with those in Reference 3 except that in the latter reference the y axis is vertical The body geometry motions and forces are defined in relation to the body coordinates x y z which can be different for each body if multiple bodies are analyzed The z axis must be vertical and positive upwards If planes of symmetry are defined for the body the origin must be on these planes of symmetry The global coordinates X Y Z are defined with Z 0 in the plane of the undisturbed free surface and the Z axis positive upwards The body coordinates for each body are related to the global coordinates by the array XBODY defined in Section 4 2 The incident wave system is defined relative to the global coordinate system and the phases of the exciting forces motions pressure and fluid velocity are defined relative to the incident wave elevation at X Y 0 These outputs are defined in the general form Re U Veio W cos wt 3 1 where W U iV is the modulus and is the phase With ref
143. In the first case you have to specify XBODY 3 Zwil to correctly position the body in WAMIT in the second case XBODY 3 will be 0 in the third case XBODY 3 will be the height of the C G above or below the waterline The WAMIT RGKernel interface tests the wetted surfaces i e the surfaces in the named Entity List or when is used for the Entity List the visible surfaces during its initialization and reports in RGKLOG TXT any case where part of a wetted surface extends above the global waterplane This usually indicates an error either in the surfaces specified as wetted or in XBODY 3 4 6 Mirror symmetry If the body has one or two planes of complete mirror symmetry it is very advantageous to mode only the independent half or quarter and use mirror symmetry options to get the rest The WAMIT RGKernel interface checks the model s symmetry flags against the ISX ISY flags specified in the GDF file and issues a warning in RGKLOG TXT if thereis any discrepancy Sometimes this can be harmless but you should check your model out to be sure you haven t either left surfaces out or covered some areas twice 4 7 Rotational symmetry An object has N fold rotational symmetry with respect to a particular axis if it is congruent to itself after a rotation of 360 N degrees about that axis Many offshore structures have complete rotational symmetry about a vertical axis For example three leg TLP s may have 3 f
144. KINIT procedure storing data about the open models 9 Error Conditions There are a number of error conditions that can occur during the initialization phase of RG2WAMIT operation If one of these occurs there will be a message at the end of RGKLOG TXT and the WAMIT run will abort The contents of RGKLOG TXT will often be helpful in identifying the problem Certain errors are also trapped during the WAMIT equation setup phase but this error handling is primarily for debugging purposes in our opinion such errors should not occur once the initialization phase has completed successfully RGKINIT error codes 0 Noerror 1 Can topen RGKINIT TXT This probably indicates that RG2WAMIT DLL and or RGKERNEL DLL arein the wrong directories They must both be installed in the same directory as WAMIT EXE 2 Unexpected end of filein RGKINIT TXT The initialization file did not contain all required information RGKINIT TXT is written by WA MIT and should not be modified by the user If the file is incomplete there s likely a bug in WAMIT If the file appears complete there s likely a bug in RG2WAMIT DLL 3 Can t open a specified model file A modd file MS2 extension named in an GDEF 2 GDF file was not found Check to see that the file exists in the same directory as the GDF file Check to see if the file name was spelled correctly in the GDF Blanks Spaces are not allowed in filenames for RG2WAMIT NOTE Filenames are not case se
145. MASS filename containing inertia matrix 2 DAMP filename containing damping matrix 2 STIF filename containing stiffness matrix NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD The separate external force data files MASS DAMP STIF contain a one line header plus the three corresponding matrices shown in the first format The first line of this file and all lines beginning with the variable NBETAH are identical to the data in Alternative 1 FRC file The data which differ in Alternative 2 are described in Section 4 4 8 5 8 3 INPUT TO FORCE IALTFRC 3 Alternative Form 3 includes one Global FRC file GFRC and N FRC files The FRC file for each body can take either the form of Alternative 1 or Alternative 2 With this option existing FRC files for single bodies can be used without modification Note however that this precludes the consideration of external mass damping and stiffness forces which produce coupling interactions between the bodies If IALTFRC 3 the input parameters in the GFRC file are listed below header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 RHO FRC 1 FRC 2 FRC N NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2
146. MZg MYg li Tho hs mzg 0 m ly Taz log MYg Mag 0 Pa To Las WAMIT equates the body mass to the mass of the displaced water in free flotation The moments of inertia are defined in terms of the corresponding radii of gyration r defined by the relation ly PYrizlrizl The array XPRDCT I J input to WAMIT contains the radii of gyration input with the same units of length as the length scale ULEN defined in the panel data file In the Alternative 2 format of the FRC file the matrices Mj Mz BE and Cz are input by the user to include the possibility of external force moment constraints acting on the body The complex amplitudes of the body s motions are obtained from the solution of the 6x6 linear system obtained by applying Newton s law 6 D u My ME Ai iw Bi BE Cy CB amp Xi j l where the matrices MZ BE and CE are included only in the Alternative 2 case Note that in the Alternative 2 case the user must specify the body inertia matrix M and include it in the total inertia matrix M Mz specified in the FRC file 3 5 The non dimensional definitions of the body motions are Ea amp AI where n 0 for i 1 2 3 and n 1 for i 4 5 6 The rotational motions amp 4 5 6 are measured in radians 3 5 HYDRODYNAMIC PRESSURE The complex unsteady hydrodynamic pressure on the body boundary or in the fluid domain is related to the velocity potential by the lineariz
147. Manager under Entity Lists This list must contain each wetted surface and only the wetted surfaces in your model or in the half quarter or sector you are modeling explicitly when using symmetry image options If you leave a wetted surface out of the list include a surface twice or include a construction surface that should not be included in the hydrodynamic solution you will very likely find volume discrepancies in WAMIT different volumes C 5 for the X Y and Z directions The interface does not currently produce a warning in these situations You can havetwo or more Entity Lists in your model They like all other entities will be distinguished by their unique names By changing the Entity List name specified in the GDF file you can conveniently switch from one Entity List to another without touching the model in MultiSurf For example you may have two sets of wetted surfaces representing two different drafts Some surfaces can be common between these lists e g surfaces that are fully wetted at the lightest draft or the lists might be completely disjoint Note that in this scenario you will need to also change XBODY 3 when the draft changes 4 3 Order of patches The ordering of patches for the WA MIT solution will often be immaterial but in some situations it matters For example if you wish to usethe NPATCH parameter in the GDF file to exclude one or more patches such as a free surface patch in order to compare
148. N 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 RHO XCG 1 YCG 1 ZCG 1 XCG 2 YCG 2 ZCG 2 XCG N YCG N ZCG N IMASS EXMASS 1 1 EXMASS 1 2 EXMASS 1 NDFR EXMASS 2 1 EXMASS 2 2 EXMASS 2 NDFR EXMASS NDFR 1 EXMASS NDFR 2 EXMASS NDFR NDFR IDAMP EXDAMP 1 1 EXDAMP 1 2 EXDAMP 1 NDFR EXDAMP 2 1 EXDAMP 2 2 EXDAMP 2 NDFR EXDAMP NDFR 1 EXDAMP NDFR 2 EXDAMP NDFR NDFR ISTIF EXSTIF 1 1 EXSTIF 1 2 EXSTIF 1 NDFR EXSTIF 2 1 EXSTIF 2 2 EXSTIF 2 NDFR EXSTIF NDFR 1 EXSTIF NDFR 2 EXSTIF NDFR NDFR NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD As in Section 4 4 the integers IMASS IDAMP ISTIF are set equal to one if the ma trix follows and equal to zero if no corresponding external matrix is included in the file Omitting the matrix is equivalent to including the matrix with zero values for all elements 8 4 The same format can be used with the external force matrices in separate files and with the corresponding filenames replacing the matrices in the FRC file This option is specified by the values IMASS IDAMP ISTIF 2 header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 RHO XCG 1 YCG 1 ZCG 1 XCG 2 YCG 2 ZCG 2 XCG N YCG N ZCG N 2
149. NBDYW are the indices for NBDYW wavemakers NRBODY NBDYP NBDYW is the total number of bodies identified in the input files and IBODYW NBDYP 1 is the index of the first wavemaker body input in the configuration files Only the radiation problems are solved when wavemakers are present including radi ation from the wavemakers as generalized modes Outputs with wavemakers include the added mass and damping matrices Option 1 a surrogate for the Haskind exciting force to be explained below Option 2 RAO s in response to the Option 2 exciting force and moment Option 4 as well as Options 5 6 7 The surrogate exciting force is the force and moment acting on the body due to the motions of the wavemakers computed from the cross coupling added mass and damping coefficients where one mode is for the body and the other mode is for the wavemaker The 12 13 outputs for the exciting force Option 2 and RAO Option 4 are the same as for incident waves except that the index of the wavemaker is output in place of the wave incidence angle BETA These wavemaker RAO s cannot be compared directly with the conventional incident wave RAO s since the amplitude of the waves generated by the wavemaker modes are not used to normalize the RAO s It is possible to make a separate run without the bodies to measure the wave elevations at the locations of the bodies using Option 6 as one might do to calibrate the wavemakers in a physical wavetank
150. NCPU gt 1 when this is available on the system permits substantial reduction in run times See Section 14 6 NEWMDS is an integer parameter specifying the number of generalized modes for each body The default value is NEWMDS 0 See Chapter 9 NFIELD LARGE is an integer parameter specifying the option to evaluate the hydro dynamic pressure and or velocity at very large arrays of field points separately from the other outputs as explained in Section 14 9 NFIELD LARGE 0 Field outputs are evaluated in the period loop with other FORCE outputs NFIELD_LARGE 1 Field outputs are evaluated in a separate loop after the other FORCE outputs The default value is NFIELD LARGE 0 NMODESFSP is an integer array used to specify the number of modes used to define the pressure distribution on free surface pressure surfaces Further details are given in Section 125 NOOUT is an integer array with length 9 used to control the output to the OUT file Each element of the array corresponds to one of the 9 options in FRC If the element equals 0 the corresponding output is omitted from the OUT file NOOUT I 0 Omit the output corresponding to IOPTN I in the OUT file NOOUT I 1 Include the output corresponding to IOPTN I in the OUT file If NOOUT is included in the configuration file all 9 integers must be specified An example is shown on the next line which specifies that all outputs are included in the OUT file except the pressures and or
151. NG Input file testi2 spl TEST12 spl cylinder R 1 T 0 5 analytic geometry npatch 3 4 2 NU NV Patch 1 side u azimuthal v vertical 4 2 NU NV Parch 2 bottom u azimuthal v radial 4 4 NU NV Parch 3 interior free surface RESET NV 2 FOR STANDARD Input file testi2 frc TEST12 FRC Cylinder R 1 T 0 5 igdef 1 irr 1 dd dt dd Ss 0 TR 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 50 O 1 5 0 0 5 end of file A 13 MULTIPLE BODIES TEST13 This test uses the same cylinder and spheroid as in the low order TEST05 The geometry is defined by the input files TEST13C GDF and TEST138 GDF TEST13C uses IGDEF 1 as in TEST1la TEST13S GDF uses the ELLIPSOID subroutine IGDEF 4 with the semi axes 2 0 0 25 0 25 specified The same separate FRC files TEST05C TESTOSS are used with IALTFRC 3 The vector IALTFRCN is included in TEST13 CFG to indicate that IALTFRC 1 in the separate FRC files for each body Normally it is necessary to duplicate the FRC files for analogous runs as for example in TESTO1 and TEST11 since the output filenames are assigned based on the FRC filename This is not necessary for individual FRC files for each body when multiple bodies are analyzed since these do not affect the output filenames The option is used to evaluate the mean drift force and moment using a control sur face following the instructions in Chapter
152. NTROL SURFACE FILE In the higher order method the first part of the CSF file is as follows header 1 ILOWHICSF ISXCSF ISYCSF NPATCSF ICDEF PSZCSF Subsequent data may be included in the CSF file after these four lines depending on the manner in which the geometry of the control surface is represented in the same manner as for the GDF file See Sections 7 5 7 8 header ISXCSF and ISYCSF are the same as those in the CSF file for ILOWHI 0 above NPATCSF is equal to the number of patches used to describe the control surface If one or two planes of symmetry are specified NPATCSF is the number of patches required to discretize a half or one quadrant of the whole of the control surface respectively ICDEF is an integer parameter which is used to specify the manner in which the geometry of the control surface is defined Four specific cases are relevant ICDEF 0 The geometry of each patch is a flat quadrilateral with vertices listed in the CSF file cf Section 7 5 ICDEF 1 The geometry of each patch is represented by B splines with the correspond ing data in the CSF file cf Section 7 6 ICDEF 2 The geometry is defined by inputs from a MultiSurf ms2 file cf Section 7 7 ICDEF lt 0 or gt 2 The geometry of each patch is represented explicitly by a subroutine in the library GEOMXACT with optional data in the CSF file cf Section 7 8 In the last case ICDEF lt 0 or gt 2 the parameter ICDEF is used in
153. Newman and P D Sclavounos The Computation of Wave Loads on Large Offshore Structures BOSS 88 Conference Trondheim Norway 1988 R Eatock Taylor and E R Jefferys Variability of Hydrodynamic Load Predictions for a Tension Leg Platform Ocean Engineering Vol 13 No 5 pp 449 490 1986 DOI X Zhu Irregular Frequency Removal from the Boundary Integral Equation for the Wave body Problem Master Thesis Dept of Ocean Eng MIT 1994 Link CH Lee J N Newman M H Kim amp D K P Yue The computation of second order wave loads OMAE 91 Conference Stavanger Norway 1991 C H Lee and J N Newman First and second order wave effects on a submerged spheroid Journal of Ship Research 1991 J N Newman The approximation of free surface Green functions in Wave Asymp totics P A Martin amp G R Wickham editors Cambridge University Press 1992 ISBN 9780521414142 Link J N Newman and C H Lee Sensitivity of wave loads to the discretization of bodies BOSS 92 London England 1992 J N Newman Wave effects on deformable bodies Applied Ocean Research 16 1 47 59 1994 DOI 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 C H Lee and X Zhu Second order diffraction and radiation solutions on floating bodies Sth Int l Workshop on Water Waves and Floating Bodies St John s New foundla
154. ODY gt 1 the data for each body is listed separately in succession identified by the body number and JALTFRCN If IALTFRC 2 the global force matrices are listed after the separate data for each body The dimension of these matrices is equal to the number of degrees of freedom as explained in Sections 4 4 and 8 2 3 5 7 AUXILIARY OUTPUT FILES FOR THE GEOMETRY Options exist to generate three auxiliary geometry output files gdf pan dat gdf pat dat and gdf low gdf Here gdf is the filename of the GDF input file For a run with NBODY gt 1 the GDF filename for the first body is used The files gdf pan dat and gdf_pat dat contain the Cartesian coordinates of panels or patches in formats suitable for perspective plotting with programs such as Tecplot This facilitates the use of perspective plots to illustrate and check the GDF inputs Examples of these plots are included in Appendix A for each test run The file gdf _low gdf is a low oder GDF file with the coordinates of new low order panels which are derived from the input geometry In all cases the coordinates are dimensional and defined in the same units as specified in the input GDF file s The data in gdf low gdf has the same definitions and format as a conventional low order GDF file Section 6 1 The coordinates of the panel vertices are defined with respect to the body coordinate system corresponding to the original GDF inputs If NBODY gt 1 the file gdf low gdf represents the body id
155. ONAL INPUT AND OUTPUT DATA In the WAMIT output files all of the output data is nondimensional except for the wave period Definitions of the nondimensional outputs are given in Chapter 3 The wave period defined in seconds has the same dimension as y ULEN GRAV where the parameters ULEN and GRAV are input in the GDF file Since the hydrodynamic force coefficients and other outputs from WAMIT are nondimensional and the frequency w has the dimension of inverse time it follows that the impulse response functions defined by equations 13 3 13 4 and 13 8 are all dimensional with the dimension of inverse time The additional impulse response functions in the output file KR1 defined as the time derivatives of the IRF s Lij have the dimension of inverse time squared For Options 1 4 the normalized outputs from F2T are defined as follows Option 1 Lyt a A w Aij 00 cos wt dw Ai B w sin wt dw _ 1 po Options 2 3 Kit f Re X w cos wt Im X w sin wt dw 0 L 1 6 E Option 4 Kit f Re w cos wt Im w sin wt dw 0 L In these equations the nondimensional frequency domain parameters are defined in Sections 3 2 4 For Options 5 and 6 the pressure and velocities are of diffraction type when INUMOPT5 6 0 In this case the normalized outputs from F2T are defined as follows 1 oo Options 5p 6p Ki f Re p w cos wt Im p w sin wt dw 0 Options 5vx 6vx K t i Re V w
156. ONUMAP 1 defines a quadratic radial mapping on the interior free surface with finer discretization close to the waterline so that the interior and exterior discretizations are similar at this point ELLIPSOID defines an ellipsoid with semi axes A B C floating with its center in the plane of the free surface C is equal to the draft If A B C RADIUS the results are identical to using SPHERE The semi axes A B and C coincide with the x y and z axis of the body coordinate system respectively BARGE defines a rectangular barge with length equal to 2x HALFLEN and beam equal to 2x HALFBEAM In the simplest case NPATCH 3 patches are used to represent the end side and bottom on one quadrant If NPATCH 1 and DRAFT 0 0 only the bot tom is represented corresponding to a rectangular lid in the free surface If NPATCH 2 and DRAFT HBOT the barge is a bottom mounted rectangular caisson If NPATCH 4 the interior free surface is included for use with the irregular frequency option IRR 1 The longitudinal and transverse directions coincide with the x and y axis of the body coordinate system respectively BARGEMP defines a rectangular barge with a rectangular moonpool at its center The moonpool is bounded by vertical walls x XMP and y YMP Other dimensions are the same as for BARGE In the normal case NPATCH 6 separate patches are on the end and side two patches on the bottom and two patches for the moonpool walls Optionally if N
157. PATCH 7 the moonpool free surface is represented by an additional patch this is an alternate scheme for the analysis of moonpools using generalized modes to describe the free surface so that resonant modes can be damped TEST17B illustrates this scheme The longitudinal and transverse directions coincide with the x and y axis of the body coordinate system respectively CYLMP defines a spar type structure consisting of a circular cylinder with a concentric moonpool of constant radius RADMP In the normal case NPATCH 3 separate patches are on the outer side of the cylinder on the bottom and on the interior wall of the moon pool Optionally if NPATCH 4 the moonpool free surface is represented by an additional patch this is an alternate scheme for the analysis of moonpools using generalized modes to describe the free surface so that resonant modes can be damped TEST17B gives a description of this scheme The optional parameter INONUMAP can be input in the GDF file to control nonuniform mapping INONUMAP 1 or INONUMAP 2 or to replace the 7 18 flat bottom by a semi circular profile INONUMAP 3 The latter option is useful to avoid sharp corners TORUS defines a floating or submerged torus as illustrated in Figure 7 4 The sections of the torus are circles of radius RCIRC with their axes on a circle of radius RAXIS in the horizontal plane z ZAXIS If RCIRC lt ZAZIS lt RCIRC the torus is floating and if ZAXIS lt RAXIS the torus is
158. RAV 1 1 ISX ISY 2 1 NPATCH IGDEF 2 NLINES 1 0 0 5 RADIUS DRAFT 1 INONUMAP nonuniform mapping Input file TEST11b spl 4 2 4 2 testilb spl cylinder R 1 T 0 5 analytic geometry npatch 2 NU NV Patch 1 side u azimuthal v vertical NU NV Parch 2 bottom u azimuthal v radial Input file testilb frc TEST11B FRC Cylinder R 1 T 0 5 igdef 1 1 1 1 1 3 3 0 2 2 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 50 O 1 5 0 0 5 end of file Input file testiic cfg TEST11c CFG Cylinder R 1 T 0 5 igdef 2 ILOWHI 1 IRR 0 ISOLVE 2 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 Input file testiic pot TEST11C POT Cylinder R 1 T 0 5 igdef 2 ie 1 1 IRAD IDIFF 2 NPER array PER follows 8 971402 2 006403 2 NBETA array BETA follows 0 45 1 NBODY testlic gdf 0 0 0 0 XBODY 1 1 1 1 1 1 IMODE 1 6 Input file testiic gdf TEST11 cylinder R 1 T 0 5 MultiSurf ms2 input nonuniform mapping 1 9 80665 ULEN GRAV Ts 21 ISX ISY 0 2 NPATCH IGDEF 3 NLINES TEST11C MS2 wetted surfs 0 0 O default settings FAST DivMult outward normal Input file testiic spl TEST1ic spl cylinder R 1 T 0 5 MultiSurf geometry npatch 2 42 NU NV Patch 1 side u azimuthal v vertical 4 2 NU NV Parch 2 bottom u azimuthal v radial Input file testilc frc TEST11C FRC Cylinder R 1 T 0 5 igdef 2
159. SC TLP fine Elastic column Spar with strakes Spar with strakes Circular cylinder Circular cylinder Circular cylinder Circular cylinder Circular cylinder Cylinder amp spheroid Cylinder amp spheroid ISSC TLP ISSC TLP Semi sub Elastic barge Elastic barge Cylinder amp moonpool Cylinder amp moonpool Cylinder amp moonpool Cylinder amp moonpool Elastic column Catamaran barge MultiSurf barge Spar with strakes FPSO with 2 tanks FPSO with 2 tanks FPSO with 2 tanks Bank of wavemakers Motions of a hinged vessel ACV with two pressure chambers ILOWHI other parameters 0 ererrrrerrererererrrerrerrrrrrerrrrrrrrrroDooD0DoD0DoDoDoDODODODODOD ODO OO Ha ITRIMWL 1 IRR 3 ISOR 1 IWALLy0 1 NBODY 2 NBODY 2 ISx 1 NPAN 128 NPAN 1012 NEWMDS 4 NPDIPOLE 673 960 ITRIMWL 1 IGDEF 1 IGDEF 1 IGDEF 1 INONUMAP 1 IGDEF 2 IGDEF 1 INONUMAP 0 IRR 1 NBODY 2 NBODY 2 ITRIMWL 1 IGDEF 9 NPER 101 IPERIN 2 IGDEF 10 IGDEF 5 NEWMDS 8 IGDEF 0 NEWMDS 8 IGDEF 7 IGDEF 7 NEWMDS 2 IDAMP 0 IGDEF 7 NEWMDS 2 IDAMP 1 IGDEF 7 NMODESFSP 1 IGDEF 1 NEWMDS 4 IGDEF 0 IGDEF 2 IGDEF 12 NPDIPOLE 2 4 6 IGDEF 21 NPTANK 8 11 12 15 ITRIMWL 1 XTRIM 1 0 0 0 15 0 ITRIMWL 1 XBODY 3 1 2 IGDEF 0 ISOLVE 1 NEWMDS 8 IGDEF 32 NEWMDS 4 IGDEF 0 NMODESFSP 2 In all of the test runs metric units are used and the gravitational acceleration is set equal to 9 80665 meters per second
160. SPAR with three strakes igdef 12 1 1 1 1 0 3 0 2 0 0 000000 VCG 100 000000 0000000 0000000 0000000 100 000000 0000000 0000000 0000000 10 000000 XPRDCT 0 NBETAH 2 NFIELD 23 0 0 15 15 0 5 end of file A 22 FPSO WITH TWO INTERNAL TANKS TEST22 The subroutine FPSOINT IGDEF 21 is used to generate the FPSO with two internal tanks with the dimensions specified in TEST22 GDF One plane of symmetry is specified about y 0 The tanks are rectangular and the vertices of each patch are specified in TEST22 GDF Both tanks have the same length 2m breadth 4 2m and depth 1 1m The aft side of tank 1 and the forward side of tank 2 are in the same plane x 0 0 The free surface of tank 1 is at z 1 1m above the plane of the exterior free surface The free surface of tank 2 is at z 0 0 The first and last patches of each tank are assigned by the parameter NPTANK Both tanks contain fluid of relative density 1 0 as specified in TEST22 CFG The parameter ITANKFPT 1 is used so that the field points can be assigned in each tank on the last two lines of TEST22 FRC Option 7 is used to evaluate the mean drift force and moment using a control sur face The control surface surrounding the FPSO is automatic defined by the input file test22 csf The parameter PSZCSF is negative indicating that the subdivision of the control surface is determined by the parameters in the file TEST22 CSP A second CSF file is contained in t
161. Section 3 1 The restoring coefficients for i j gt 7 are defined as Sp Except as noted below there are no other restoring coefficients If the configuration parameter ICCFSP 1 is assigned additional external restoring coefficients are included which represent the force on the body if there is a chamber of constant volume enclosing the pressure surface with the assumption that compressibility effects are negligible In this case the pressure in the chamber acts both on the water below 15 20 and on the body above the chamber to give additional forces and moments on the body The only nonzero external restoring coefficients are Ci3 C35 pg n ds Sp Cia Cai pg If niyds Cis Csi pg If nds 15 78 15 21 REFERENCES 10 11 12 13 J N Newman Algorithms for the Free Surface Green Function Journal of Engi neering Mathematics Vol 19 pp 57 67 1985 DOI J N Newman Distribution of Sources and Dipoles over a Quadrilateral Journal of Engineering Mathematics Vol 20 pp 113 126 1986 DOI J N Newman Marine Hydrodynamics MIT Press 1977 Link J N Newman The Drift Force and Moment on Ships in Waves Journal of Ship Research Vol 11 pp 51 60 1967 F T Korsmeyer C H Lee J N Newman and P D Sclavounos The Analysis of Wave Effects on Tension Leg Platforms Invited paper of OMAE 88 Conference Houston TX 1988 J N
162. TN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 VCG XPRDCT 1 1 XPRDCT 1 2 XPRDCT 1 3 XPRDCT 2 1 XPRDCT 2 2 XPRDCT 2 3 XPRDCT 3 1 XPRDCT 3 2 XPRDCT 3 3 NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIFLD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD NFIELD_ARRAYS ITANKFLD 1 NFX 1 X1 1 DELX 1 NFY 1 Y1 1 DELY 1 NFZ 1 Z1 1 DELZ 1 ITANKFLD 2 NFX 2 X1 2 DELX 2 NFY 2 Y1 2 DELY 2 NFZ 2 Z1 2 DELZ 2 ITANKFLD NFIELD_ARRAYS NFX NFIELD ARRAYS X1 NFIELD ARRAYS DELX NFIELD_ ARRAYS NFY NFIELD_ARRAYS Y1 NFIELD ARRAYS DELY NFIELD_ ARRAYS NFZ NFIELD_ARRAYS Z1 NFIELD ARRAYS DELZ NFIELD ARRAYS The additional data is defined as follows NFIELD ARRAYS is the number of separate arrays NFIELD ARRAYS must be an integer greater than or equal to zero ITANKFLD n n 1 2 NFIELD ARRAYS is an integer which specifies if the array n is in the exterior fluid domain or in an internal tank ITANKFLD 0 denotes the exterior fluid domain In cases where the field point array is in an internal tank ITANKFLD is assigned with the same integer as the number of the tank as explained in Section 12 1 If no internal tanks are included ITANKFLD 0 must be specified NFX NEY NFZ are positive integers specifying the number of elements in the array parallel to the X Y Z axes The total number of elem
163. The triangles are discretized by quadrilateral panels two sides of each panel are on the lines from the centroid to the nodes from the 10 3 SEG ene cairn A LV N i ISSA SAIA KZ ASS SA NOSES SES NS Sis ESSAS NASA LS e ve A Se RR DA o 4 a a ae SRH ta Figure 10 1 Automatic discretizations on the interior free surface of a circular cylinder The figure on the left shows the result of the discretization algorithm used when ISOR 0 The figure on the right shows the result of the special algorithm used when ISOR 1 to ensure continuity of the panels adjacent to the waterline waterline segments to the centroid with more dense discretization toward the waterline The last panel is a small triangle which is used in the subsequent part of the program as a flag indicating the end of the connectivity In this way the connectivity is guaranteed between certain groups of panels starting from quadrilateral panels contiguous to waterline segment This option should not be used for any body where a ray from the centroid of the waterplane area intersects the waterline more than once In that case the option IRR 1 should be used When the option IRR 3 is used special care is required in preparing the GDF file to ensure that there are no significant gaps between the vertices of adjacent panels at the waterline In addition it is desirable to avoid panels at the waterline which are of extremely small dimension
164. U NV 4 2 interior fs NU NV Input file testi3a frc TEST13a FRC Cylinder spheroid trimmed waterlines 1 1 1 1 0 3 0 1 1 1 0 test05c frc test05s frc A 14 ISSC TLP TEST14 The subroutine TLP IGDEF 9 is used to generate the ISSC TLP with the dimensions specified in TEST14 GDF Except for the geometry the inputs correspond to the low order test runs TESTO6 and TESTOT As explained in Appendix A 6 a warning message is displayed for Options 8 and 9 since IDIFF 0 For TEST14a TEST14a CFG TEST14a POT and TEST14a FRC are used to output data to be used as input to F2T TEST14 GDF and TEST14 SPL are used without change TEST14a POT has zero and infinite frequencies and 99 uniformly spaced additional fre quencies IPERIN 2 is specified in the cfg file In FRC IOPTN A4 is set to output the RAOs in all six modes Since there are a large number of wave frequencies in TEST 14a it is a good example of the benefit of multiple processors See Section 14 6 The runtimes in this case using NCPU 1 2 4 8 are almost inversely proportional to NCPU Input file test14 cfg TEST14 CFG ISSC TLP ILOWHI 1 ipltdat 5 ILOWHI 1 IRR 0 ISOLVE 1 IQUADI 4 IQUADO 3 KSPLIN 3 NUMHDR 1 IALTFRC 2 Input file test14 pot TEST14 ISSC TLP ILOWHI 1 450 0 0 IRAD IDIFF 3 NPER array PER follows 5 10 15 1 NBETA array BETA follows O 1 NBODY test14 gdf 0 0 0 0 XBODY 1 0 10 1 20 IMODE 1 6 Input file test14
165. WA MIT interface for WA MIT version 6 4 include e Dipole patches Section 4 15 e Internal tanks Section 4 16 e Control surfaces for mean drift forces Section 4 17 e Transparent treatment of breaklines in MultiSurf surfaces Section 4 12 e Allowing NPATCH Oin the short GDF file Section 5 e Short GDF format for low order analysis Section 6 C 2 1 2 New Features for WAMIT version 7 0 New features introduced to the RG2WA MIT interface for WA MIT version 7 0 include e Free surface Pressure patches Section 4 15 e Internal tanks Section 4 16 2 Supported features and options The WAMIT RGKernel interface supports all current features of the higher order solution option Multiple bodies Each body is associated with a GDF file in the POT or FNAMES file IGDEF 2 is reserved to mean geometry specified by an MS2 file The different bodies can have various IGDEF types XBODY positioning Each body has an associated XBODY transformation to position it in the global coordinate system The MultiSurf model of a body can be constructed in any convenient position e g aligned and centered in the body coordinate system Alternatively one MultiSurf mode can be constructed with two or more bodies in their final global positions this allows visualization of the bodies relative and absolute positioning Mirror symmetry If the body has mirror symmetry with respect to one vertical plane only one half of the body needs to
166. _demo exe can be used for demonstration purposes without obtaining an end user license subject to the conditions stated in the website The installation and use of this software are the same as the licensed version with the following exceptions e The program only accepts geometry inputs from the standard input files for the test runs described in the Appendix e The license identification file userid wam and some DLL files are not required e The program runs are interrupted after display of the header and the user is prompted to press the Enter key to continue the run The msi installer file includes all of the input files required to execute the standard test runs To begin the install of WAMIT DEMO using the msi installer simply double click the msi file and proceed with the installation as shown in Figure 2 3 Click Next to begin the installation setup For the install to proceed the main installation directory folder needs to be defined as shown in Figure 2 4 The recommended name is c WAMITv7DEMO but the user may prefer to use a different drive or directory name with a maximum length of 40 characters for the string This directory should be accessible by all users on the computer First time installs of WAMIT DEMO that will not be using MultiSurf for WAMIT click Next to begin the installation process Users that will be installing MultiSurf for WAMIT should uncheck the checkbox labeled I am not using AeroHydro MultiSur
167. a further powerful capability for constructing parametric model families A variable can serve as a parameter in the GDF file Irregular frequency removal Interior free surface patches can be constructed in MultiSurf and included in the data available to WA MIT for use with its IRR 1 option 3 Required files versions and file locations RG2WAMIT DLL contains the Fortran C interface code RGKERNEL DLL is the relational geometry C library RGKERNEL DLL is acomponent of any MultiSurf or SurfaceWorks installation however please NOTE The WAMIT RG Kernel interface may use a different RG Kernel version from M ultiSurf These DLL versions are not necessarily interchangeable and should be kept in separate directories Although they have the same filename different DLL versions can be distinguished by different sizes and different dates This said it has been our uniform experience to date that a newer version of RGKERNEL DLL can be safely substituted for an older one RG2WAMIT DLL does NOT have to be recompiled in this event and new modeling features incorporated in the newer RGKERNEL DLL become available for use with WAMIT RG2WAMIT DLL and RGKERNEL DLL must be located in the same folder as WAMIT EXE Also any mode file named in an IGDEF 2 GDF must be located in the same folder as the GDF We ll subsequently refer to this folder as the working folder MultiSurf does not need to be running when the WAMIT run takes place WAMIT does
168. a eene eea Sn Dela aeiee ioanen eea E SEES e SNe es 8 4 7 Rotational Symmetry cos aea e E E aa E EEE E Sp EN ER anent 8 4 8 Fast vs Accurate evaluation sois senise enn eee Serea a Eea R o e Seesen 9 4 9 Divisions and Subdivisions sinnn A E E a E RE EE 9 4 10 Irregular frequency removal sinesi an e E i E E a E a 10 4 11 Coordinate singul ritieSks niniin aan a E A e a meat an aai 10 4 12 Br aklines in surface Serri Giaa a a A a a A E E E saas 11 4 13 COSME spacing menns snapin r ESE EA aE E EEE E E E EEEa 11 ATA Parameters ennnen siaa rE TE AE E T TEE E T E A TE A 12 4 15 Patch typesand color coding eseis enais e EE EE E a E E EES aa 12 ATO internal tank S nonna a E ETE E E E E Aa 13 4 17 Control surfaces for mean drift forces sesssssessseseesesseeeesstseesteserstestesessesetsseserstesersesseenessreeesee 13 SAED AiO aA TE E E EE A 14 6 Short GDF format for low order analysis 022 222 seseests teeters tetas een eesti eae 16 7 POG TIE RGIK POG TX crann e alae ned sta a dia aati alin 16 8 SyNOpSis OF operati ON iiiaio aaia erate Rap ASen 17 9 Error GONG MOMS cas casted cesta cetera ED ias 18 1 Introduction A joint development effort between AeroH ydro Inc and WAMIT Inc has forged an intimate connection between M ultiSurf and WAMIT Asaresult model geometry developed in MultiSurf s relational geometry RG framework can be directly accessed by WAMIT for all setup and analysis purposes within WAMIT s
169. ace as explained in Chapter 11 and Section 15 9 IALTCSF 1 use Alternative 1 IALTCSF 2 use Alternative 2 The default value is IALTCSF 1 IALTFRC is an integer specifying the alternative forms of the FRC file as explained in Sections 4 3 4 4 and 8 3 5 IALTFRC 1 use the Alternative Form 1 FRC format shown in Section 4 3 IALTFRC 2 use the Alternative Form 2 FRC format shown in Section 4 4 IALTFRC 3 use the Alternative Form 3 FRC format shown in Section 8 5 The default value is IALTFRC 1 IBODYW is an integer specifying the body number of the first body which represents a wavemaker in a wall see Section 12 3 The default value is IBODYW 0 No wavemakers are present in walls ICCFSP is an integer specifying the option to exclude or include the external restor ing coefficients due to the pressure acting on closed chambers above free surface pressure surfaces see Section 12 5 The default value is ICCFSP 0 Do not include the external restoring coefficients IDELFILES is an integer specifying the option to delete and overwrite old output files with the same filenames as explained in Section 5 1 and Section 5 10 IDELFILES 1 overwrite old P2F file without interactive prompt IDELFILES 2 overwrite old P2F and OUT files without interactive prompts IDELFILES 3 overwrite old P2F file and delete new P2F file IDELFILES 4 overwrite old P2F and OUT files and delete new P2F file The default value is IDELFILES 0 IF
170. al number of panels including both conventional and dipole types The dipole panels may be located arbitrarily within the array of all panels It is possible to analyze bodies which consist entirely of zero thickness elements by including the line NPDIPOLE 1 nn in the CFG file where nn NPAN is the same integer value input in the GDF file The source formulation cannot be used if dipole panels are included Thus the fluid velocity on the body cannot be evaluated and the mean drift force moment can only be evaluated by the momentum or control surface methods Options 7 and 8 A symmetry plane can be used when there are flat thin elements represented by dipole panels on the plane of symmetry As an example when a keel on the centerplane y 0 is represented by dipole panels either the port or starboard side of the vessel can be defined in the GDF file with ISY 1 6 9 Chapter 7 THE HIGHER ORDER METHOD ILOWHI 1 The higher order method is fundamentally different from the low order panel method de scribed in Chapter 6 The body geometry can be represented by different techniques including flat panels B spline approximations geometry models developed in MultiSurf and explicit analytical formulae The velocity potential on the body is represented by B splines in a continuous manner and the fluid velocity on the body is evaluated by ana lytical differentiation In most applications this provides a more accurate solution with a sm
171. al annular free surface with interior boundary an ellipse with semi axes AI BI The center of the ellipsoid is at the origin of the body coordinate system ISXCSF 1 and ISYCSF 1 should be specified in the CSF file This subroutine is used for the spheroid in TEST13 ELLIPSOID CS NOSYM defines a complete ellipsoidal outer control surface and an nular free surface The center of the waterplane is shifted by XS YS ZS relative to the body coordinate system ISXCSF 0 and ISYCSF 0 should be specified in the CSF file In these subroutines the parametric coordinate U is related to the polar angle about the vertical axis and the parameteric coordinate V is related to the radial coordinates on the free surface and bottom and the vertical coordinate on the side of the cylinder 11 4 COMBINING TWO CONTROL SURFACE FILES In some cases it is convenient to use separate CSF files to represent the inner part on the free surface and the outer part which forms the remainder of the closed control surface below the free surface For example a low order surface is generally used when the body surface is defined by low order panels in order to provide a good fit at the waterline On the other hand a higher order outer surface has the advantage of more efficient integration using Gauss quadratures to reduce the computational time Thus in this situation it may be advantageous to use ILOWHICSF 0 for the inner free surface and ILOWHICSF 1 for the outer part
172. alent sets of input data in lines 7 and 8 of the POT file 4 10 8 NBETA 0 0 45 0 90 0 135 0 180 0 225 0 270 0 315 0 BETA array and 8 NBETA 0 0 45 0 BETA 1 increment NBODY is the number of bodies Except for the analysis of multiple bodies Chapter 8 NBODY 1 GDF K is the name of the Geometric Data File of the Ath body XBODY 1 K XBODY 2 K XBODY 3 K are the dimensional X Y Z coordi nates of the origin of the body fixed coordinate system of the kth body relative to the global coordinate system as shown in Figure 4 1 in the same units of length as ULEN The global coordinate system is required when walls are present Section 12 4 and when multiple bodies are analyzed Chapter 8 The global coordinate system is also used in place of the body coordinate system to define field point data fluid pressures velocities and free surface elevation Normally in the absence of walls or multiple bodies the coordi nates XBODY 1 and YBODY 1 should be set equal to zero unless it is desired to refer the field point data to a different coordinate system from that of the body The incident wave velocity potential is defined relative to the global coordinate system Consequently the phases of the exciting forces motions hydrodynamic pressure and field velocity induced by the incident wave are defined relative to the incident wave elevation at X Y 0 XBODY 4 K is the angle in degrees of the axis of the body coordin
173. aller number of unknowns compared to the low order method A brief outline of the method is provided in Sections 7 1 7 3 to give the necessary back ground for several input parameters which must be specified This includes the subdivision of the body surface into patches the further subdivision of the patches into panels and the use of B splines to develop approximations on these surfaces It is important to note in this context that a panel is not restricted to be a flat quadrilateral in physical space but can be a general surface in space with continuous curvature to fit the corresponding portion of the body as precisely as is appropriate The number of patches NPATCH is specified in the GDF file Various options exist to specify the other input parameters which determine the number or size of the panels order of the B splines and order of the Gauss quadratures used to integrate over each panel Section 7 4 describes the data in the Geometric Data File GDF which is common to all applications of the higher order method Sections 7 5 7 8 describe the four different options for describing the body geometry and the corresponding inputs Section 7 9 describes the procedure for modifying the GEOMXACT subroutine to represent the geometry of user specified bodies If the body has thin elements there are two possible approaches as in the analogous case of low order panels described in Chapter 6 The first is to represent both sides of these eleme
174. aluated either from the Haskind relations or direct pressure integrals as defined in Section 3 3 with the surface integrals extended over the ensemble of the central body and its images 5 A ship with a discontinuous shearing mode at the midship section which can be used in conjunction with the fixed mode option described in Section 4 5 to evaluate the shear force acting on the hull In cases such as examples 3 and 5 above where the modes are discontinuous it is important when the higher order method is used ILOWHI 1 for the mode discontinuities to coincide with the boundaries between patches and not to occur within the interior of patches as explained in Section 7 1 9 2 In the generalized mode analysis one or two planes of geometric symmetry can be ex ploited to reduce the computational burden when the body geometry permits In such cases it is necessary to define the generalized modes to be either symmetrical or antisym metrical These symmetries must be specified in the subroutine by assigning one of the integers 1 6 to the array ISYM for each of the generalized modes The value of this integer signifies that the symmetries of the generalized mode are the same as the corre sponding rigid body mode Since the symmetries of surge j 1 and pitch j 5 are always the same and likewise for sway j 2 and roll j 4 specifying ISYM 1 or 5 is equivalent and similarly ISYM 2 or 4 is equivalent If there are no planes of symmetry any
175. ames files as follows copy testtst wam fnames wam as explained in Chapter 2 Alternatively the batch file runtests bat can be used to run all tests in succession A 1 TRUNCATED VERTICAL CYLINDER TESTO1 The added mass and damping coefficients exciting forces motions wave elevations field pressures field velocities and drift forces are evaluated for a freely floating truncated ver tical circular cylinder of radius 1 meter and draft 0 5 meters in infinite water depth for three wave periods and one wave heading The origin of the coordinate system is located at the intersection of the vertical axis of the cylinder and the undisturbed position of the free surface Using two planes of symmetry only the first quadrant of the surface of the cylinder is discretized with 256 panels 16 8 and 8 panels are distributed in the azimuthal radial and vertical directions with equal spacing The characteristic length is set equal to the radius of the cylinder The cylinder center of gravity is located at the origin of the coordinate system and the radii of gyration relative to its axes are taken equal to 1 meter In TESTO1A the option to trim the waterline is specified with the parameters ITRIMWL and XTRIM included in the TESTO1A CFG file The other input files are unchanged but the filenames TESTO1A POT and TESTO1A FRC are used so that the output files will be named accordingly The cylinder is rotated 15 degrees about the x axis and elevated
176. amitv7 Edit the first line to show the actual number of CPU s on the system and save the edited file with the same name With this change the total run time for all of the standard tests should be substantially reduced Test14a is a particularly good example as noted in Appendix A 14 Instructions for finding the number of CPU s on the system are in Section 14 6 Depending on the size of the system RAM it may be appropriate to change the parameter RAMGBMAX following the guidelines in Section 14 3 The value 0 5 is sufficient for all of the test runs unless NCPU is greater than 16 For older systems with less than 1Mb of RAM the parameter RAMGBMAX should be reduced to about half of the available RAM 2 8 MEMORY AND STORAGE RESTRICTIONS WAMIT uses scratch files on the hard disk for temporary storage at runtime Depending on the run parameters the total number of scratch files and or their size may become quite large Normally these files are deleted by WAMIT after the files are no longer needed and before the program stops However some PC Windows configurations save these deleted files in a recycled directory and this can cause the hard disk to become overloaded Users who experience this problem should delete the accumulated files in the recycled directory or alternatively change their system setup to avoid saving a backup of all deleted files 2 9 2 9 MODIFYING THE INPUT FILES A text editor can be used to edit the input fi
177. an one in absolute value absolute differences are used otherwise relative differences are used The maximum number of iterations is controlled by the parameter MAXMIT 5 12 in the configuration files With the default value MAXMIT 8 the maximum number of integration ordinates is 28 256 When necessary this parameter can be increased but it should be noted that this increases the computational time exponentially when the mean drift force and moment are evaluated from Option 8 Since the components of the mean drift force are nondimensionalized by ULEN and the moment by ULEN convergence can also be affected by the choice of ULEN in the GDF file If ULEN is much smaller than the physical length scale of the body it will not affect the convergence tests and vice versa Another point to note is that some components of the force and moment may be relatively small and of little practical importance whereas they may affect the convergence test When in doubt about situations where the warning message occurs it may be advisable to increase MAXMIT by 1 or 2 units and compare the resulting outputs manually Starting in Version 7 0 an option can be used to issue a warning message and to output in the file wamitlog txt all points on the body surface where the magnitude of the nondimensional fluid velocity is greater than VMAXOPT9 during the evaluation of the mean drift force and moment from pressure integration on the body surface In this case i
178. and 26 without the assumption of energy conservation This permits the analysis of cases where the body motions are affected by non conservative effects such as external damping The azimuthal integration required to evaluate the momentum flux is performed by an adaptive quadrature formula The integration is performed iteratively with convergence specified by the criterion of absolute or relative errors in each drift force less than TOL 10 The maximum number of iterations is controlled by the parameter MAXMIT A warning message is displayed in the event that this convergence criterion is not satisfied See Section 5 8 for further information regarding the interpretation and control of this warning message Often the warning message is issued because the length scale parameter ULEN is much smaller than the relevant length scale of the body Since the drift force increases in pro portion to length and the moment in proportion to length relatively small differences between large values may not be significant In this case the warning message can be avoided by increasing ULEN to a value more representative of the length This force or moment can be either converged for most practical purposes or too small to be important in practice It is recommended to check the practical importance of this quan tity Further check on the convergence of the result can be made by increasing MAXMIT gradually Since the computational time increases exponentia
179. and v respectively or by the parameter IQUADO in the configuration files The order of the basis functions are specified by the parameters KU and KV in the SPL file or KSPLIN in the configuration files The inner integrations in u in equations 15 33 and 15 34 are carried out as described below for each abscissa of the Gaussian quadrature for the outer integral up The integration of the regular part of the wave source potential is carried out by Gauss Legendre quadrature The order of the inner quadrature is specified by the input parame ters IQUI and IQVI in the SPL file or by the parameter IQUADI in the configuration files Numerical tests suggest that the order of the quadratures should be one order higher than the order of the basis functions The integrals involving the Rankine source and normal dipole are evaluated in the manner explained next If the field point uy is on the panel the integrand is singular at 15 7 this point Otherwise the integrand is regular throughout the domain of the panel In the singular case the panel is subdivided into a small square subdomain centered at uy and one or more rectangular subdivisions adjoining the square as required to cover the remainder of the panel The integrals over the latter subdivisions are treated in the same manner as for the other panels where the integrand is regular The integrals where the integrand is regular are evaluated by Gauss Legendre quadra ture If the field point
180. anks along the x axis IS 1 0 is required When planes of symmetry are appropriate the following integrals which are originally evaluated over one half or one quarter of the tank with nonzero values should be set equal to zero If IS 1 1 CTANK 2 0 CTANK 4 0 CTANK 8 0 If IS 2 1 CTANK 3 0 CTANK 5 0 CTANK 8 0 All other elements are multiplied by IMUL 2 or 4 to account for the planes of symmetry in the same manner as C I J In GETIF after CALL OPHEAD to output the hydrostatic matrix for the hull the subroutine TANKFS is called when tanks are present In TANKFS the following assign ments are made for the hydrostatic restoring coefficients where the extra terms added for the tanks are summed over all tanks associated with each body C 3 3 3 3 er p CTANK 1 C 3 4 C 3 4 er p CTANK 3 C 3 5 C 3 5 or p CTANK 2 15 17 C 4 4 C 4 4 er p CTANK 9 CTANK 6 C 4 5 C 4 5 pr p CTANK 8 C 5 5 C 5 5 pr p CTANK 7 CTANK 6 Also if IALTFRC 2 C 4 6 C 4 6 pr p CTANK 4 C 5 6 C 5 6 pr p CTANK 5 The extra terms in C 4 6 and C 5 6 are omitted for a freely floating body since these are balanced by the vessel s corresponding buoyancy moments When tanks are present the header of the output file frc out includes nondimensional values of the tank volumes and the contributions from the tanks to C 3 3 C 3 4 and C 3 5 Next
181. ant storage requirement is for the NEQN influence coefficients on the left hand side of the linear systems of equations Since typical values of NEQN are between 100 and 10 000 between 10 and 108 influence coefficients must be stored for each left hand side Here we consider only the storage of these matrices since other data storage requirements are negligible by comparison The influence coefficients are related to the free surface Green function and its deriva tives as defined in Section 15 2 These include real components associated with the Rank ine source potential 1 r and complex components associated with the effect of the free surface cf Equations 15 14 18 To avoid redundant computations the real components are evaluated only once whereas the complex components must be evaluated separately for each wave period Thus separate storage is required for the real and complex matrices The estimated storage for each of these is described below WAMIT takes into account flow symmetries in setting up the linear systems to minimize NEQN When planes of symmetry exist with respect to the planes X 0 and or Y 0 NEQN can be reduced by one half in each case thus reducing the number of influence coefficients on one left hand side by a factor of 1 4 or 1 16 In general the number of left 14 5 hand sides NLHS must be increased by 2 or 4 in order to solve both the symmetric and anti symmetric problems e g heave and surge in the case
182. application this may or may not be appropriate The roll and pitch restoring coefficients C 4 4 and C 5 5 are also affected due to the term pgV 2p In special cases it may be necessary to make corrections using the external stiffness matrix in the FRC file see Section 4 4 Special attention is required to analyze body motions if the pressure acting on the FSP surface results in a static restoring force on the body referred to here as an external restoring force This will occur if the pressure is contained within a chamber such as an air cushion vehicle exerting a force and moment on the upper surface of the chamber If the volume is constant and compressibility effects are negligible the external restoring coefficients are defined by equation 15 78 If the configuration parameter ICCFSP 1 these coefficients are included in the hydrostatic matrix and in the evaluation of the RAO s This option is used in TEST25 In the default case ICCFSP 0 these coefficients are not included see Section 4 7 When FSP surfaces are included the mean drift force and moment based on momentum Option 8 and based on the use of a control surface Option 7 includes the effects of the pressure acting on the FSP surfaces However the mean drift force and moment based on pressure integration Option 9 only includes the contribution from integration over the wetted surface of the body When Option 9 is used with FSP surfaces a warning message is issued Wh
183. are defined in the subroutine WAVEMAKER in the DLL file NEWMODES F designated by the parameter IGENMDS 21 in TEST23 CFG This subroutine reads the depth of the lower edge of the wavemaker ZHINGE 2m from the file WAVEMAKER DEPTH DAT Wave elevations are evaluated at a square array of 64 field points defined in TEST23 FRC using the uniform field point array option in Section 3 10 Input file test23 cfg TEST23 CFG 8 wavemaker segments in wall x 0 ILOWHI 1 IALTFRC 2 ISOLVE 1 skip POTEN solutions for wavemakers in walls MONITR 0 NUMHDR 1 IGENMDS 21 use NEWMODES subroutine WAVEMAKER PANEL_SIZE 1 use default spl parameters INUMOPT6 1 output separate radiation modes in 6 file IFIELD_ARRAYS 1 field points input in array format in frc file ipltdat 4 NEWMDS 8 Input file test23 pot TEST23 POT 8 wavemaker segments in wall x 0 4 fluid depth 0 1 IRAD IDIFF 2 NPER array PER follows Dio As 1 NBETA array BETA follows 0 0 1 NBODY test23 gdf 0 0 0 0 XBODY 0 0 0 0 0 0 IMODE 1 6 First 10 lines of input file test23 gdf TEST23 GDF wavemaker 8 segments in wall x 0 2 lt y lt 10m ISY 1 1 9 80665 ULEN GRAV 1 1 ISX ISY 8 0 NPATCH IGDEF 0 0000 2 000000 2 00000 0 0000 3 00000 2 00000 0 0000 3 00000 0 000000 0 0000 2 000000 0 000000 end of Patch 1 0 0000 3 000000 2 00000 0 0000 4 00000 2 00000 Input file TEST23 FRC field point wave elevations IALTFRC 2 no external forces 0 0 0 0 0
184. are generated during a typical WAMIT run These are intended to facilitate visual examination of the results in tabular form and post processing by other software The formatted output file is described in Section 5 1 This summarizes the hydrody namic outputs in a single file with appropriate identifying text The header which includes a summary of the inputs and hydrostatic computations The numeric output files de scribed in Sections 5 2 5 are intended to tabulate the hydrodynamic outputs in a more concise form for post processing The principal numeric output files are described in Sec tion 5 2 Section 5 3 explains the additional files used to output the Froude Krylov and scattering components of the exciting forces Section 5 4 describes the output file used for the B spline coefficients of the body pressure when the higher order method is used Section 5 5 explains the special output files which are generated when the pressure and velocity are evaluated at user specified points on the body Section 5 6 describes the output file for the hydrostatic restoring coefficients which are computed by WAMIT and used in the equations of motion Section 5 7 describes the auxiliary files which output geometric data Section 5 8 describes the outputs of warning and error messages The log file wamitlog txt described in Section 5 9 is intended to provide useful archival information including a condensed summary of all input files and error or warning messa
185. arning is displayed and the coordinates of the center of buoyancy are set equal to zero For bottom mounted structures where panels are not defined on the bottom VOLZ differs from the correct submerged volume by the product of the bottom area and depth Volume Coordinates of center of buoyancy 1 Tp y Jh Maas 4 F w 7 Jha neveds a a zy Jh ne dS Matrix of hydrostatic and gravitational restoring coefficients C 3 3 pg Ws nads C 3 3 C 3 3 pgL C 3 4 pg IIs ynadS C 3 4 C 3 4 pgL C 3 5 pg Js angds C 3 5 C 3 5 pgL C 4 4 pg IIs W nadS pgV2 mgz C 4 4 C 4 4 pgL C 4 5 pg tynd S C 4 5 C 4 5 pgL C 4 6 pg9Y p mgr C 4 6 C 4 6 pgL4 C 5 5 pg Io t nadS pv mgz C 5 5 C 5 5 pgL C 5 6 pgVYy mgyg C 5 6 C 5 6 pgL where C i j C 3 1 for all i j except for C 4 6 and C 5 6 For all other values of the indices i 7 C i j 0 In particular C 6 4 C 6 5 0 In C 4 4 C 4 6 C 5 5 and C 5 6 m denotes the body mass When Alternative form 1 is used for the FRC file Section 4 3 the body mass is computed from the relation m pV When Alternative form 2 is used for the FRC file Section 4 4 the body mass is defined by EXMASS 3 3 3 2 ADDED MASS AND DAMPING COEFFICIENTS a Aig yet eff nipjdS pLk J pLkw Here k 3 for i j 1 2 3 k 4 for i 1 2 3 7 4 5 6 or i 4 5 6 7 1 2 3 k for i
186. arrays The parameter Q is given by equations 14 2 3 If RAMGBMAX is sufficiently large all of the real and complex influence coefficients are stored in RAM In this case the total RAM required is estimated from Figure 14 1 with Q Q NCPU x Qe If this is not possible the program will distribute the data between RAM and the hard disk using the following order of priorities 1 real coefficients are stored on the hard disk leaving all available RAM for the storage of complex coefficients 2 if NLHS gt 1 some but not all left hand side arrays are stored in RAM and the remain der on the hard disk 3 if the RAM can not store one complete complex left hand side array a subset of the coefficients are stored in RAM and the remainder on the hard disk If multiple processors are used NCPU gt 1 all of the complex arrays must be in RAM Thus the minimum RAM required for multiple processing is estimated from Figure 14 1 with Q NCPU x Q If this is not possible execution of the program terminates with an error message advising the user to increase RAMGBMAX or reduce NCPU If NCPU 1 the following minimum requirements apply for available RAM 1 if ISOLVE 1 direct solver or ILOWHI 1 higher order method one complete com plex left hand side must be stored in RAM 14 7 2 if ISOLVE gt 1 block iterative solver one complex left hand side must be stored in RAM with dimensions equal to the maximum block size 14 5 DATA STORAGE IN SCRAT
187. assigned the extension p2f The final output from FORCE is saved in a file with the extension OUT which includes extensive text labels and summaries of the input data FORCE also writes a separate numeric output file for the data corresponding to each requested option in a more suitable form for post processing these files are distinguished by their extensions which correspond to the option numbers listed in the table in Section 4 3 4 3 Additional numeric output files are generated for the exciting forces using Option 2 or Option 3 to provide data for the separate Froude Krylov and scattering components of these forces as explained in Section 5 3 Two additional numeric files are generated when the FRC file specifies either Option 5 pressure and fluid velocity on the body surface or Option 6 pressure and fluid velocity at field points in the fluid to assist in post processing of these data For Option 5 a panel geometry file with the extension pnl is created with data to specify the area normal vector coordinates of the centroid and moment cross product for each panel on the body surface For Option 6 the field point file with the extension fpt specifies the coordinates of the field points in the fluid 4 4 4 1 SUMMARY OF CHANGES IN VERSION 7 INPUT FILES Several changes have been introduced in WAMIT Version 7 to simplify the input files and to use a more consistent notation for the numeric output files These inclu
188. ate system of the Kth body relative to the X axis of the global system defined as positive in the counterclockwise sense about the vertical axis as shown in Figure 4 1 MODE is a six element array of indices assigned for each body where I 1 2 3 correspond to the surge sway and heave translational modes along the body fixed x y z axes and 1 4 5 6 to the roll pitch and yaw rotational modes around the same axes respectively Each of these six elements should be set equal to 0 or 1 depending on whether the cor responding radiation mode s and diffraction component s are required See the options IRAD 0 and IDIFF 0 above The MODE array in the radiation solution specifies which modes of the radiation prob lem will be solved To understand the significance of the MODE array in the diffraction solution when symmetry planes are defined the complete diffraction problem is decom posed into symmetric antisymmetric components in a manner which permits the most efficient solution and when IDIFF 0 only those components of the diffraction potential required to evaluate the exciting force for the specified modes are evaluated For example if ISX 1 IDIFF 0 MODE 1 1 and the remaining elements of MODE are set equal to zero then the only component of the diffraction potential which is solved is that part which is antisymmetric in x If the complete diffraction potential is required for example to evaluate the drift forces or field data IDIFF sh
189. ately for each line Any additional text on the same lines is ignored so that comments may be inserted as in the example above The filenames on Line 2 are read as ASCII text of unknown length maximum of 256 characters all on one line and no additional comments may be included on this line The program F2T has been updated to function with output files from WAMIT Version 7 To ensure compatibility users should verify that 1 WAMIT Version 7 0 or later has been used to generate the WAMIT numeric output files and b the file f2t exe is dated after 31 December 2011 It is possible to mix earlier versions subject to the following restrictions e If output files from WAMIT Version 6 are used as inputs to the updated f2t exe set the input parameter IPEROUT 1 Post processing of field pressures and velocities is not possible unless these output files are renamed with extensions 6p 6vx 6vy 6vz e If older versions of f2t exe are used with output files from WAMIT Version 7 the default value IPEROUT 1 must be used for the WAMIT runs Post processing of field pressures and velocities is not possible unless these output files are renamed with extensions 6 7x 7y 7z 13 4 OUTPUT FILES The output files from F2T are in two complementary formats with duplication of the output data in the two formats The filename assigned to all of the output files is primary with different extensions The first set of output files have appended file
190. ation IRR 2 and ILOWHI 0 0 4 10 3 Automatic free surface discretization IRR 3 and ILOWHI 0 10 4 Automatic free surface discretization IRR 3 and ILOWHI 1 10 5 Assigning different values of IRR for NBODY gt 1 11 MEAN DRIFT FORCES USING CONTROL SURFACES 11 1 Control surface file CSF 11 2 Low order control surface file 11 3 Higher order control surface file 11 4 Combining two control surface files 11 5 Automatic control surfaces 11 6 Output 12 SPECIAL EXTENSIONS 12 1 Internal tanks 12 2 Trimmed waterlines 12 3 Radiated waves from wavemakers in tank walls 12 4 Bodies and wavemakers with vertical walls 12 5 Bodies with pressure surfaces 12 6 Integrating pressure on part of bodies 13 THE F2T UTILITY 13 1 Definitions of radiation and diffraction outputs 13 2 Acquiring input data for F2T with WAMIT 13 3 How to use F2T 13 4 Output files 13 5 Options 5 and 6 13 6 Theory 13 7 Dimensional input and output data 14 COMPUTATIONAL TOPICS 14 1 Number of equations NEQN and left hand sides NLHS 14 2 Solution of the linear systems 14 3 Temporary data storage 14 4 Data stored in RAM 14 5 Data stored in scratch files 14 6 Multiple processors NCPU gt 1 14 7 Modifying DLL files 14 8 Reserved file names 14 9 Large arrays of field points 15 THEORY 15 1 The boundary value problem 15 2 Integral equations for the velocity potential 15 3 Integral equations for the source formulation 15 4 Discretization of the integral equations in the low or
191. ay of uniformly spaced field points are defined on the free surface in the file test05a frc and the parameter IFIELD ARRAYS 1 is specified in test05a cfg Some of these field points are on or inside the body waterlines These points are identified with zero in column five in the output file test05a fpt and the outputs for the pressure and velocity are equal to zero at these points see Section 4 3 and Section 4 7 Input file test05 cfg TESTO5 CFG Cylinder spheroid NBODY 2 ILOWHI 0 IPLTDAT 1 ISOR 1 ILOG 0 IRR 0 NUMHDR 1 NOOUT 0 11101111 IALTFRC 3 Alternative Form 3 FRC IALTFRCN 1 1 Input file test05 pot TESTO5 POT Cylinder spheroid ILOWHI 0 1 0 HBOT o 0 IRAD IDIFF 2 1 5 2 0 1 0 0 2 NBODY test05c gdf 1 25 0 0 0 0 0 0 Co mb de de d test0ds gdf 0 5 0 0 0 0 90 0 RD RT Ca Co First 10 lines of input file test05c gdf Cylinder R 1 T 2 8 6 8 1 000000 9 806650 1 1 112 0 0000000E 00 0 0000000E 00 2 000000 0 0000000E 00 0 0000000E 00 2 000000 0 2538459 5 0493091E 02 2 000000 0 2588190 O0 0000000E 00 2 000000 0 2588190 O0 0000000E 00 2 000000 0 2538459 5 0493091E 02 2 000000 First 10 lines of input file test05s gdf Spheroid Slendernes 0 125 Halflength 2m 8 8 2 000000 9 806650 1 1 64 000000 961571 961571 000000 000000 961571 END HR RF ND Input file 0000000E 00 9460625E 09 5150545E 03 0000000E 00 0000000E 00 5150545E 03 testOb frc
192. be constructed If the body has mirror symmetry with respect to two orthogonal vertical planes only one quarter needs to be constructed These symmetry options are represented similarly in MultiSurf and WAMIT Rotational symmetry Alternatively rotational symmetry is supported A MultiSurf model can have rotational symmetry about any one of the coordinate axes with any number of copies NCOPIES at an angular spacing of 360 NCOPIES degrees This feature greatly simplifies modeling structures that have rotational symmetry only 1 NCOPIES of the total model needs to be explicitly constructed Units WAMIT is flexible with regard to units but some of its inputs are quantities with units of length and the global length unit is implicit in the GRAV parameter M ultiSurf supports meters centimeters millimeters feet and inches as length units and this choice is specified in the mode file The interface code compares the mode and global units and transparently performs any needed units conversions Parameters The GDF file permits overriding floating point values in the definition of any entity in the model This allows a single mode parametrically constructed to be C 3 analyzed in a wide variety of configurations without opening the model and making any changes in MultiSurf Variables and formulas Use of numeric variables and formulas in RG models is an advanced feature supported by MultiSurf versions 4 8 and higher This represents
193. cable to both methods in the same form The principal exception is the Geometric Data File which specifies the geometry of the body surface To simplify the understanding and use of this User Manual chapters are organized separately for generic information common to both methods and for specific information which refers to either the low or higher order method separately In Chapter 2 a tutorial description is given to help users get started using WAMIT in the PC Windows environment The examples described in Chapter 2 are for the simplest context of a single body 1Throughout this User Manual numbers in square brackets refer to the references listed after Chapter 15 1 1 Chapter 3 defines the various quantities which can be evaluated by WAMIT and which are contained in the output files Chapter 4 gives more detailed information regarding the generic input files including the Potential Control File POT and Force Control File FRC which specify the principal non geometric inputs for WAMIT Also described in this Chapter are the files fnames wam config wam and break wam which are useful to specify input filenames and various pa rameters or options Users of Version 6 should note that some changes have been made which are intended to make the input data more consistent As a result Version 7 may require modifications of old input files as explained in Section 4 1 Appendix B describes the utility v6v7inp which has been prepared
194. cal and their existence in the computations can be attributed primarily to the neglect of viscous damping associated with flow sep aration at the outer and inner corners of the cylinder This damping is only important when the vertical motions of the cylinder and or moonpool are large Typical resonant amplitudes are likely to be in the range represented by the dashed lines in Figure A 1 In order to damp the moonpool response and heave motions separately a different physical problem is considered where a lid is placed on the free surface of the moonpool This lid is considered to be an extension of the body surface and represented by an additional patch Thus NPATCH 4 is assigned in test17a gdf and used also in Test17b and Test17c The geomxact subroutine CYLMP assigns the patch number 4 to be the circular disc of radius RADMP in the plane Z 0 However allowance must be made for the motions of the actual free surface relative to the body This is done by defining appropriate generalized modes which are nonzero only on patch 4 The most important mode is a vertical translation assigned here in the subroutine file NEWMODES F with the index j 7 In Test17b a pitch rotation of the lid j 8 is also included to provide a more general deflection of the free surface A more complete expansion can be introduced but at the wavenumbers considered here and for head sea incidence angle these two modes of motion are sufficient These two generalized
195. ce formulation IOPTN 6 lt 0 and the mean drift force and moment from pressure integration IOPTN 9 1 or 2 For the control surface drift force and moment IOPTN 7 1 or 2 if ISOR 0 only the horizontal drift force and vertical moment can be evaluated using Alternative 1 IALTCSF 1 ISOR 1 is required for the other components using Alternative 1 and for all components using Alternative 2 Running POTEN with ISOR 1 requires substantially longer run time and larger scratch storage In the higher order method ILOWHI 1 all of the FORCE evaluations are made directly from the solution for the velocity potential and ISOR 0 is required ITANKFPT is an integer parameter specifying the option to input field point fpt coor dinates in the fre control file either in the conventional format default or in the format required when some or all of the field points are located within internal tanks The default value ITANKFPT 0 should be used except in cases where tanks are included with field points inside the tanks ITANKFPT 0 All field points are in the exterior domain Field points are input as specified in Sections 4 3 and 4 4 with the coordinates of each field point on one line or using the array format described in Section 4 11 ITANKFPT 1 Field points are listed in the fre control file with the tank number preceding the coordinates Thus in place of the XFIELD lines shown in Section 4 3 the correponding data are input as follows ITANK
196. ces and other partition boundaries if any must be included after this in the file The vertex coordinates X Y must be ordered so the partition boundaries enclose the waterlines in the counter clockwise direction as illustrated in the examples below In cases where there are no planes of symmetry each waterline is a closed curve which must be surrounded by a closed partition boundary When there is more than one waterline the partition boundaries must not overlap nor should gaps exist between them 11 11 In cases where the body is symmetric about X 0 and or Y 0 and the same symmetry planes are used for the CSF the completeness of the partition boundaries depends on whether or not the waterline intersects the planes of symmetry If the waterline is entirely within the interior of a quadrant or half space and does not intersect the symmetry plane s then it must be completely enclosed by a partition boundary If the waterline intersects a symmetry plane then the partition boundary should not include that plane since it will be closed by reflection about the plane For patches on the free surface the parametric coordinates are defined with U 1 on the body waterline and U 1 on the outer partition boundary V is positive in the counter clockwise direction around body waterline When a circular cylindrical outer surface is used IPARTR 1 U is in the azimuthal direction and V is in the vertical direction on the side and radial direc
197. ces are input in the CSF file an error message is issued and the run is terminated NPATCSF must be equal to zero or less than zero NPATCSF 0 the control surface is automatic and includes the intermediate free surface NPATCSF lt 0 the control surface is automatic and the intermediate free surface is omitted ICDEF must be equal to zero ICDEF 0 the control surface is automatic RADIUS is the parameter which controls the radius of a circular outer surface or specifies that the outer surface is quadrilateral RADIUS gt o0 the outer surface is a circular cylinder of this radius RADIUS lt O0 the boundary of the outer surface is quadrilateral with NV 1 vertices speci fied by the coordinates X 1 n Y 1 n n 1 2 NV 1 DEPTH is the depth of the control surface This must be a positive real number greater than the maximum depth draft of the body NPART is an integer which specifies the number of partition boundaries Each partition boundary includes NV vertices defined by the coordinates X Y Partition boundaries are required for two possible purposes a to define the outer boundary of a quadrilateral control surface and b to separate multiple waterlines If the body has only one waterline and the outer boundary is circular NPART 0 If the body has only one waterline and the outer boundary is a quadrilateral NPART 1 When the outer boundary is a quadrilateral its vertices must be defined by the first partition with NV 1 verti
198. ch are the same for most or all runs and to use cfg with an appropriate filename to specify inputs which are specific to that particular run Thus the file config wam delivered with the 2 1 standard test runs includes the parameters RAMGBMAX NCPU and USERID_PATH which are the same for all test runs the other parameters required for each run are input in the separate files test cfg 2 1 INSTALLATION AND SETUP The PC executable Version 7PC is installed as a msi install package The naming conven tion for this package is wamit_v7nnn_x64w_t msi where nnn represents the version number and release version 7 101 is v7101 and t is the package distribution 1 for lease versions and s for site versions To begin the install of WAMIT using the msi installer simply double click the msi file and proceed with the installation as shown in Figure 2 1 Click Next to begin the installation setup 2 WAMITv Setup ij Welcome to the WAMITv7 Setup Wizard The Setup Wizard will install WAMITv7 on your computer Click Next to continue or Cancel to exit the Setup Wizard Back Next Cancel Figure 2 1 Initial startup window of WAMIT msi installer for both lease and site licenses For the install to proceed the user must choose one of three install modes as shown in Figure 2 2 The Typical install will install the complete software package First time installs of WAMIT that will not be using MultiSurf fo
199. cial attention is required unless different subroutines are used for each body or all of the bodies using the same subroutine have identical dimensions Most of the existing GEOMXACT subroutines read in the appropriate dimensions from the GDF file in scalar form to initialize parameters within the subroutine for subsequent calls If the same subroutine is initialized again for another body the dimensions are overwritten As a result the dimensions in the last GDF file are applied to all of the bodies using the same subroutine In cases where bodies with different dimensions are represented by the same subroutine the dimensions used in subsequent calls should be saved within the subroutine as arrays with dimension NBODY The subroutine FPSO12 in GEOMXACT illustrates this procedure for two FPSO hulls with different dimensions A warning message is issued if two or more bodies use the same value of IGDEF in GEOMXACT There are three alternative ways to input parameters to the FORCE subprogram Al ternative Form 1 can be used for freely floating bodies and the more general Alternative 2 Form can be used for bodies subject to external forces Alternative 3 includes a Global Force Control file GFRC and a separate FRC file for each body each being in either Form 1 or 2 These three alternative are described respectively in Sections 8 1 8 2 and 8 3 The POT file is as shown in Section 4 2 with the last three lines of data repeated in sequence for eac
200. cial inputs are required when pressures and or velocities are evaluated for field points inside the tanks Option 6 In this case when the field point coordinates XFIELD are input as explained in Section 4 3 the parameter ITANKFPT 1 must be specified in the cfg file as explained in Section 4 7 and the format of the XFIELD inputs in the fre file must include the corresponding number of each tank or zero for the exterior domain When all of the field points are defined by arrays using the option described in Section 4 11 the parameter ITANKFPT is not used and may be deleted from the cfg file Inputs which relate to the body s mass including VCG and the radii of gyration XPRDCT IALTFRC 1 or XCG YCG ZCG and the inertia matrix EXMASS IALTFRC 2 refer to the mass of the body alone without the tanks or with the tanks empty The same definitions apply to the outputs of these quantities in the mmx file described in Section 5 6 and in the log file wamitlog txt When IALTFRC 1 is used the body mass is derived from the displaced fluid mass corresponding to the body volume minus the fluid mass in the tanks The body volumes center of buoyancy and hydrostatic restoring coefficients displayed in the header of the out file are calculated from the exterior wetted surface of the body and are not affected by the tanks The volumes densities values of ZTANKFS and hydrostatic restoring coefficients for the tanks are listed separately after the
201. clude additional real numbers in columns 6 and 7 Important rules which must be followed in preparing the external RAO file are as follows e If header lines are included in the numeric output files NUMHDR 1 a header line must be included in frc rao Conversely if header lines are not included in the numeric output files NUMHDR 0 a header line must not be included in fre rao e For each wave period heading and mode index a separate line or successive lines must be included in frc rao with the same set of data including two or four real numbers which define the modulus phase real and imaginary components of each RAO e The wave periods heading angles and mode indices must be the same as in frc rao 4 46 and these must be in the same order with respect to period and heading angles the order of mode indices is arbitrary The precise format of the data in frc rao is not important and does not need to be identical to frc 4 with respect to column widths spaces or number of decimal digits This file is read with FORTRAN free format read statements so that the data can be input in integer fixed or floating point formats It is recommended to use only integer format for the mode index and fixed or floating point format for all other data If the data cannot be read or is not consistent with the file frc 4 an error message is issued and the program execution is terminated There are two exceptions where the data in frc rao do not
202. cluding the intermediate free surface for bodies with circular or elliptical waterlines The following table lists these subroutines which are described in more detail below ICDEF SUBROUTINE NPATCH CSF INPUTS 1001 CCYL_CS 3 RADIUS DRAFT RADIUSI 1002 CCYL_CS_NOSYSM 3 RADIUS DRAFT RADIUSI XS YS ZS 1003 ELLIPSOID_CS 2 A B C ALBI 1004 ELLIPSOID_CS_NOSYM 2 A B C ALBI XS YS ZS The last column indicates the dimensions and other input parameters to be included in the GDF file Where two or more lines of inputs is shown in the table the CSF file should follow the same format as illustrated in the test runs Brief descriptions of each subroutine are given below More specific information is included in the comments of each subroutine CCYL_CS defines one quadrant of a circular cylindrical control surface of outer radius RADIUS and depth DRAFT The inner boundary of the free surface is bounded by a circular body waterline of radius RADIUSI ISXCSF 1 and ISYCSF 1 should be specified in the CSF file This subroutine is used for the circular cylinder in TEST13 CCYL_CS_NOSYSM defines the entire curface of a circular cylindrical control surface as described above for subroutine CCYL_CS The center of the waterplane is shifted by XS YS ZS relative to the body coordinate system ISXCSF 0 and ISYCSF 0 should be specified in the CSF file ELLIPSOID_CS defines one quadrant of an ellipsoidal outer control surface with semi axes A B C plus an elliptic
203. cobi polynomials uz q v7 0 w 0 9 4 ug 6g 5q vg 0 we 0 9 5 ug 28q 429 159 v9 0 w9 0 9 6 Here NEWMDS 3 and q z HBOT 1 is the normalized vertical coordinate varying from 0 at the bottom to 1 at the free surface 3 Two bodies connected by a simple hinge joint at the origin permitting each body to pitch independently about the y axis In this case the six rigid body modes are defined as if the hinge is rigid and the new mode j 7 is specified by the vector u7 en sen z v7 0 wr lelny 9 7 with NEWMDS 1 Here sgn x is equal to 1 according as x gt 0 or x lt 0 Test 24 described in Appendix A 24 is a more complicated example with multiple hinges 4 An array of five identical bodies all described by panels in the same GDF file as if for a single body with five separate elements the bodies are centered at transverse positions y 4w 2w 0 2w 4w to simulate images of the central body in the presence of tank walls at y w The surge heave and pitch exciting forces on the central body are then specified by the exciting force coefficients X7 Xg X9 The corresponding new modes are defined which have the same normal velocities on the central body and zero on the images Here NEWMDS 3 and the vectors uj vj wj are all zero except in the range w lt y lt w where w 9 8 ws 1 9 9 Ug Z Wo z 9 10 With these definitions the exciting force coefficients can be ev
204. consider the inertia forces and moments due to the body mass If IALTFRC 1 the body mass m is calculated from VOL and all of the inertia coefficients are propotional to m Since VOL is the total displaced volume of the hull the static mass of the fluid in the tanks is included in m However the same inertia effects are represented more correctly for dynamic conditions by the added mass of the tank to be discussed be low For this reason if IALTFRC 1 the mass matrix BFRCND is reduced by the sum gt pr p xVOLTANK VOLM where the sum is over all tanks Likewise the terms mgz in the restoring coefficients C 4 4 and C 5 5 are reduced If IALTFRC 2 these correc tions are not made and the external mass matrix should exclude the fluid in the tanks If IALTFRC 1 the radii of gyration should be estimated ignoring the fluid in the tanks The added mass and damping coefficients are evaluated globally by integrating the corresponding components of the pressure over both the external hull surface and the internal tank surfaces The only modification for tank panels patches is to multiply their contributions by RHOTANK the relative density of the tank fluid compared to the external fluid Since there is no radiation from the tanks the damping coefficients should be zero In test calculations they are generally very small except near tank resonances A useful check is to verify that the damping coefficients of the hull with tanks are equal to the
205. correspond with the data in frc 4 If the parameter IBODYW gt 0 is assigned in the CFG file to define one or more wavemakers the modes for these wavemakers must not be included in the external RAO file Similarly if fixed modes of the body are defined in the FRC file as explained in Section 4 5 and designated by negative mode indices in frc 4 these modes must not be included in the external RAO file Users are advised not to use fixed modes in combination with the option to define RAO s in the external RAO file since the modified RAO s cannot be used to evaluate the fixed mode loads A warning message is issued in this case It is not necessary to use IREADRAO 1 in place of IREADRAO 0 but this avoids unnecessary computations for Options 5 9 when the RAO s will be modified by the user 4 14 EVALUATING FORCE OUTPUTS IN POTEN IFORCE 2 In the default case where IPOTEN 1 and IFORCE 1 WAMIT first executes the POTEN subroutines to evaluate the potential for all wave periods and then the FORCE subroutines to evaluate the output parameters specified in the FRC control file as shown in the flow chart in Figure 1 1 In that case the output parameters are included in the frc OUT file and also in the separate numeric output files which use either the filename frc in the default case NUMNAMS 0 or alternatively the filename optn if NUMNAM 1 In long runs where the execution time for POTEN is large no FORCE outputs are available until afte
206. cos wt Im V w sin wt dw 0 Here p is the nondimensional total pressure defined in Section 3 5 and V is the nondi mensional total velocity vector defined in Section 3 7 When INUMOPT5 6 1 the separate components of the diffraction and radiation potentials and velocities are output by WAMIT and transformed by F2T In this case the normalized outputs from F2T are defined as follows 1 oo Options 5p 6p Kp t f Re pp w cos wt Im pp w sin wt dw 0 K t F Re p w G 00 cos wt dw F manoda 1 sx _ Options 5vx 6vx Kat f Re VEp w coswt Im V p w sin wt dw 0 Kot Re Vw V c0 cos wt dw im V w sin wt dw In these equations the nondimensional frequency domain functions are defined in Sec tions 3 5 and 3 7 Note in the transforms K that the frequency domain functions and 13 8 V V differ from the corresponding outputs in the WAMIT numeric output files by the factor 1 KL Thus before applying the Fourier integrations of these functions in F2T the WAMIT outputs are divided by KL w L g where L ULEN and g GRAV In all other cases above the frequency domain functions are the same as the WAMIT outputs in the corresponding numeric output files Chapter 14 COMPUTATIONAL TOPICS In this Chapter various topics are covered which affect the use of WAMIT especially for more advanced applications with complicated geometry or multiple structures These require a la
207. creases To avoid this singularity in the discretized problem the panel size should be of the same order as the thickness or smaller in order to render the linear system well conditioned Thus the size of the linear system becomes large as the thickness decreases An alternative form which is nonsingular can be obtained from Green s integral equa tion for the limit when the thickness is zero In this modified form of the integral equation the velocity potential is represented by a distribution of dipoles only without sources The dipole strength is equal to the difference of the velocity potential on two opposite sides of the zero thickness surface denoted by Aq below If the body surface S consists partly of thin dipole elements Sg and partly of con ventional source elements S which are represented by both sources and dipoles Green s integral equations 15 11 13 and the dipole distribution can be combined in the following form Omg x Guds AGG nde I n GneGaS 15 46 when x is on the conventional body surface S and 6G renee A6Gn nodSE Ar n A bncGing 15 47 when x is on the surface of zero thickness Sy 15 10 Instructions for using this option are in Sections 6 3 and 7 10 TEST09 and TEST 21 described in Appendix A are examples of its use It should be emphasized that thin dipole elements must be submerged in contact with the fluid on both sides A thin element whic
208. cted with outward normals There are no parameter lines in this example 6 Short G DF format for low order analysis Beginning with WAMIT version 6 4 the short GDF format used for IGDEF 2 higher order analysis can also be used for low order analysis ILOWHI 0 The format is almost exactly the same as detailed in the previous section for higher order analysis The only difference is that the first token on line 4 must be 0 in place of NPATCH the number of patches RG2WAMIT will calculate the number of panels from the model geometry the sum of panel counts over the wetted surface patches Advantages of this feature are 1 No long form low order GDF file needs to be created 2 Parameter lines can be used in the short GDF file to vary the geometry at WA MIT run time 3 Trimmed surfaces triangle meshes and composite surfaces can be freely used along with other surface types for low order analysis Note that a MultiSurf model that is suitable for higher order analysis may not be 100 percent suitable for low order analysis The primary issue is divisions and subdivisions which control the subdivision of surfaces into panels A surface with very low divisions x subdivisions can be plenty accurate for higher order analysis but would result in very few panels This aspect should be investigated and divisions increased if necessary CountPanels command will likely be a useful tool in such an investigation 7 Log fileRGKLOG TXT
209. cy domain input data for F2T is evaluated by WAMIT The algorithms used to evaluate the Fourier transforms in F2T require that the input data is restricted to a uniformly spaced set of frequencies w nAw where n 1 2 3 NPER When radiation IRFs are evaluated it is necessary to also evaluate the corresponding frequency domain outputs for w 0 and wy4 using the inputs PER lt 0 0 and PER 0 0 respectively See Section 4 2 In the WAMIT run this is done most easily by setting the parameter IPERIN 2 in the configuration files inputs are radian frequencies and by using the option to write the data NPER and w1 Aw on the lines normally used to specify NPER and the array PER The input files used for the tests of the ISSC TLP can be regarded as an example These files are listed in Appendix Al4a They are essentially the same as for TEST14 with the exception of IPERIN 2 and the specification of the input frequencies When the input files to F2T are read the data is sorted so that the frequencies are listed in ascending order regardless of their order in the WAMIT output files Thus the order of the periods 1 0 0 0 is irrelevant and it is possible to patch together two or more separate sets of output files from WAMIT e g one with a coarse set of wave frequencies and the other with intermediate frequencies to provide a finer set without concern regarding their order 13 3 HOW TO USE F2T The program F2T can be executed after
210. d body surfaces for both TESTO9 and TEST09a The dipole panels are red Input file test09 cfg TESTO9 CFG Spar with three strakes ilowgdf 1 ipltdat 5 ISOR 0 ISOLVE 0 ISCATT 1 ILOG 0 IRR 0 MONITR 0 NUMHDR 1 IPERIN 3 IPEROUT 3 NOOUT 111101111 NPDIPOLE 673 960 Input file test09 pot TESTO9 POT Spar with three strakes HBOT 1 1 IRAD IDIFF 3 NPER array PER follows 0 1 0 5 1 0 2 NBETA array BETA follows 0 0 45 end of file 1 NBODY test09 gdf 0 0 0 0 HBOT XBODY 1 4 1 chet E O tea IMODE 1 6 First 10 lines of input file test09 gdf SPAR R D W T NS TWIST 18 00 200 00 3 70 0 000000 3 1 000 18 00000 9 806650 0 0 960 18 00000 0 Q0000000E 00 0 0000000E 00 17 38667 4 658743 8 333333 15 58846 9 000000 8 333333 17 38667 4 658743 0 0000000E 00 17 38667 4 658743 8 333333 15 58846 9 000000 16 66667 Input file test09 frc TESTO9 FRC Spar with three strakes 1 1 1 1 1 3 0 2 0 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 23 0 0 15 15 0 5 end of file Input file test09a cfg TESTO9a CFG Spar with trimmed waterline ISOLVE 0 ISCATT 1 ILOG 0 IRR 0 MONITR 0 NUMHDR 1 IPERIN 3 IPEROUT 3 NOOUT 111101111 ITRIMWL 1 XTRIM 10 10 0 NPDIPOLE 673 960 Input file test09a pot TESTO9A POT spar trimmed waterline 1 HBOT 1 1 IRAD IDIFF 3 NPER
211. d to as panels Note that while these panels are flat and rectangular in parametric space they are unrestricted in physical space except for the requirement that they represent a subdivided element of the corresponding patch Thus in general these panels are curved surfaces in physical space In some references such as 22 panels are called sub patches or simply patches Figure 7 2 shows the example where the side and bottom of the shaded quadrant in Figure 7 1 are each subdivided into four panels In addition to the requirement of geometric continuity within the domain of each patch it is also necessary that the hydrodynamic solution should be continuous in the same domain For this reason if discontinous generalized modes are used as in Test24 described in Appendix A 24 the modal discontinuities should coincide with boundaries between adjacent patches Figure 7 2 Subdivision of one quadrant of the cylinder shown in Figure 6 1 into panels In this case N N 2 on both patches 7 2 B SPLINE REPRESENTATION OF THE SOLUTION The other important subject to consider is the manner in which the velocity potential is represented on each patch Desirable properties of this representation are that it should be smooth and continuous corresponding to the physical solution for the fluid flow over the surface with control over the accuracy B splines are used for this purpose More specifically the velocity potential is represent
212. d to run executable code compiled with IVF libifcoremd dll libmmd d1l libiomp md dil msvcri00 dlil svml dispmd dll These DLL files are distributed by Intel and may be redistributed to all users Copies of these files are included with each distribution of WAMIT Users may encounter a problem on some older PC systems indicated by the runtime error message The system cannot execute the specified program This problem can be overcome by downloading and in stalling the Microsoft Visual C 2005 Redistributable Package which is available from Microsoft 2 4 After the install is complete a Program Folder will appear in the Start Menu called WAMIT v7 This has links to the README file manual and shortcut to wamit bat which opens a command window in the WAMIT install directory Users wishing to set up a specific run environment for WAMIT can edit wamit bat with any text editor To enable easy access to the WAMIT executable directory copy the shortcut in the Program Folder to the Desktop To authenticate the install the user must copy the WAMIT supplied userid wam file to the install directory Users that have lease licenses must also execute the instructions outlined in the README_LEASE txt file provided in their distribution to complete their activation step 2 2 DEMONSTRATION PROGRAMS A special demonstration version of WAMIT can be downloaded as a msi install pack age from the web site www wamit com This program wamit
213. damping coefficients without tanks Special attention is required for the vertical modes heave roll pitch where there is a fictitious hydrostatic contribution to the added mass First consider heave where the relevant boundary conditions are n3 on Sp and Ko 0 on the free surface Here K w g Thus the heave potential is given by ds z 1 K where z is a local vertical coordinate with its origin in the tank free surface The heave added mass coefficient is Ass p A nadadS Nr Cr 3 3 9K 15 66 Ag Bl yn3 zno dadS pV rye Cr 3 4 gk 15 67 15 18 ee A em 27g bad rte Cr 3 5 9 15 68 Since w gK the last terms are cancelled by the hydrostatic restoring coefficients Thus in the limit w 0 there are no contributions to the equations of motion for the LHS elements associated with the vertical force or vertical translation as expected on physical grounds In the classical hydrostatic analysis of ships the tank free surface effect is evaluated by considering the second moments of the tank free surface about a local origin at the centroid of the free surface whereas in the expressions for Cy these moments are about the global origin This difference can also be explained in terms of the corresponding added mass coefficients in an analogous manner to the analysis above 15 11 BODIES WITH PRESSURE SURFACES The boundary value problem described in Section 15 1 is extended h
214. de the following e The POT file designated as Alternative Form 1 in Version 6 is not supported The POT file designated as Alternative Form 2 in Version 6 must be used with two exceptions 1 the option to include the parameter IRR on line 2 is not supported and 2 the parameter NEWMDS is removed from the POT file If IRR and or NEWMDS is nonzero the value s must be input in the configuration file e The parameters IQUAD and IDIAG which controlled the accuracy of integration over panels in the low order method are no longer used In Version 7 the integration is performed in the same manner as for IQUAD 0 IDIAG 1 in older versions e Options 6 formerly field pressure and 7 formerly field velocity are modified in the FRC file and in the corresponding numeric output files Option 6 is used for both the field pressure and velocity in a similar manner as for Option 5 body pressure and velocity The numeric output files for these are designated by the extensions 6p 6vx 6vy 6vz replacing the old extensions 6 7x 7y 7z e Option 7 is used for the mean drift force and moment using a control surface replacing the old CFG parameter ICTRSURF The corresponding numeric output file extension is 7 replacing the old extension 9c e Dipole panels or patches must be identified in the configuration file following the same format as in Version 6 The option to identify these elements in the GDF file is not supported e Wal
215. de to input the values of the normal velocity for each generalized mode at the centroid of each body panel DEFMOD includes a short sub routine DEFINE which can be modified by the user for each application In the DEFMOD subroutine as provided DEFINE evaluates the bending modes of the vertical column used in TESTO8 The same subroutine is included in NEWMODES and used for TEST18 The four examples itemized in the introduction of this Chapter are included in separate files DEFINE 1 DEFINE 2 DEFINE 3 and DEFINE 4 to illustrate the preparation of appropriate subroutines Additional modes are included in these files The evaluation of the normal velocity 9 1 for generalized modes requires a specification of the vectors u v w and normal components nz Ny nz at the centroid of each panel The first WAMIT run is aborted after writing these data to a file and also the panel areas which are required to evaluate the hydrostatic coefficients for the generalized modes The user is then requested to run DEFMOD After DEFMOD is run WAMIT may then be re run to complete the analysis in the normal manner This procedure is described in greater detail below and illustrated by the flow chart in Figure 9 1 There are two input output files associated with DEFMOD both denoted by the filename gdf of the GDF file The file gdf PRE for PRE processing contains for each panel the centroid coordinates x the area and the six components of n and x x n The f
216. defined Since NEWMODES is contained in a DLL file it can be modified by the user in a similar manner to the GEOMXACT file for defining bodies analytically cf Section 7 9 The first method using the program DEFMOD can be used with any suitable FOR TRAN compiler Three separate runs must be made first with WAMIT to set up the input file for DEFMOD then with DEFMOD and finally with WAMIT to solve for the potentials in the usual manner In the second method only one run of WAMIT is re quired however users of the PC executable code must compile the DLL file following the instructions below In Section 9 1 the input files are described for performing the generalized mode analysis for a single body Section 9 2 describes the use of DEFMOD and Section 9 3 describes the alternative use of the DLL file NEWMODES The definitions of hydrostatic restoring coefficients are described in Section 9 4 and the analysis of multiple bodies NBODY gt 1 is described in Section 9 5 Several test runs are used to illustrate the use of generalized modes including the use of both DEFMOD and NEWMODES and the appropriate input files TESTOS ILOWHI 0 9 3 and TEST 18 ILOWHI 1 analyze a bottom mounted column with bending modes TEST 16 analyzes a rectangular barge with bending modes TEST17 a b illustrates the use of gen eralized modes to analyze damped motions of a moonpool TEST23 uses generalized modes to analyse a bank of paddle wavemakers TEST24
217. degrees XTRIM 2 3 are Euler angles with the convention that the body is first pitched about the transverse y axis and then rolled about the longitudinal axis Yaw can be included via XBODY 4 With this convention the projection of the axis on the plane Z 0 is at the same angle XBODY 4 as the projection of the x axis In the low order method ILOWHI 0 the input panels from the GDF file are tested for their positions relative to the plane of the free surface Z 0 Dry panels which are entirely above the free surface are removed from the array of panel coordinates within the program Wet panels which are entirely submerged are retained without modification Panels which intersect the waterline referred to as waterline panels are trimmed at the waterline In some cases where waterline panels have three vertices below the free surface and one vertex above the free surface the resulting trimmed panel is a polygon with five sides in these cases the panel is subdivided to form two separate panels one quadrilateral and one triangular The number of panels is increased by one for each subdivided panel Converesely when dry panels are removed the number of panels is decreased Examples of subdivided panels can be seen in the perspective plot corresponding to TESTO1A in Appendix A In the higher order method ILOWHI 1 an analogous procedure is followed for each patch of the body based on the vertical positions of t
218. depending on the options used are listed in the Introduction to Chapter 4 Note that the P2F file output from POTEN is given the same filename as the input control file with the extension p2f The P2F file may be saved and reused for various applications of the FORCE module where the same velocity potentials apply The output file from FORCE is given the same filename as the force control file with the extension out Asterisks x denote the extensions corresponding to each option in the numeric output files as listed in the table in Section 4 3 1 6 1 2 CHANGES INTRODUCED IN Version 7 0 New features which are included starting in Version 7 0 are outlined below e For runs where NBODY gt 1 global planes of symmetry can be used if the body geom etry is suitable see Section 8 5 e When the higher order method ILOWHI 1 is used patch data are output in the wamitlog txt file if NPER 0 to assist in checking the geometry e Part or all of the boundary surface associated with the bodies can be defined as a free surface with oscillatory pressure distribution see Section 12 5 e The mean drift forces can be evaluated using control surfaces without evaluating the same forces from pressure integration see Chapter 11 e When the mean drift forces are evaluated from pressure integration points where the velocity on the body surface exceeds a specified limit can be output in the file wamitlog txt using the parameter VMAXOPT9 in the CFG fil
219. der method ILOWHI 0 15 5 Discretization of the integral equations in the higher order method ILOWHI 1 15 6 Removal of irregular frequencies 15 7 Integral equations for bodies with thin submerged elements 15 8 Mean drift forces based on pressure integration 15 9 Mean drift forces using control surfaces 0 5 15 10 Internal tank effects 15 11 Pressure surfaces APPENDIX A DESCRIPTION OF TEST RUNS A 1 Truncated vertical cylinder TESTO1 A 2 Irregular frequency removal 2 A 3 Local pressure drift force TESTOR A 4 Body near a wall TE A A 5 Multiple bodies TESTIS A 6 The ISSC Tension Leg Platform TEST06 A 7 The ISSC Tension Leg Platform TEST07 A 8 Elastic column with gene modes TEST08 A 9 Spar with three strakes TESTO9 A 11 Higher order analysis of circular cylinder TEST11 12 Irregular frequency removal TEST12 A 13 Multiple bodies Sra 20 MultiSurf Barge TE Spar with A 22 FPSO with two internal one retin A 23 Radiated wave field from a bank of wavemakers TEST23 A 24 Motions of a hinged vessel TEST24 A 25 Air cushion vessel with pressure chambers TEST25 APPENDIX B FILE CONVERSION USING THE UTILITY v 6v7inp APPENDIX C USING THE WAMIT RGKERNEL INTERFACE By J S Letcher Jr 0 6 Chapter 1 INTRODUCTION WAMIT Version 7 is a radiation diffraction panel program developed for the linear analysis of the interaction of surface waves with various types of f
220. dices equal to zero This will not give the correct vertical drift force on the body however since the components of the diffraction potential and body motions which are odd functions of x and y have not been evaluated In general the drift forces should be evaluated only after evaluating all components of the first order potential i e by setting IDIFF 1 for the stationary body and IRAD 1 and IDIFF 1 for the freely floating body in the POT file An example of a valid short cut exists if both the body geometry and the hydrodynamic flow field are symmetrical about a plane of symmetry then it is not necessary to evaluate first order potentials which are odd about that plane since these would vanish For example if the body is symmetrical about y 0 and the incident wave heading angle is either zero or 180 the drift force and moment can be obtained by setting MODE n 0 for n 2 4 6 To calculate the mean drift forces it is necessary to evaluate the runup or equivalently the velocity potential at the waterline Since the program utilizes the velocity potentials at the centroids of the panels adjacent to the waterline for the runup it is advisable to use panels with small vertical dimensions near the waterline 6 7 6 3 BODIES WITH THIN SUBMERGED ELEMENTS Bodies which consist partially or completely of elements with small or zero thickness can be analysed by defining these elements as dipole panels The geometry of these elements i
221. different values of ILOWHICSF can be used for multiple bodies as illustrated in TESTOS One or two planes of symmetry can be used to simplify the definition of the control surface as specified by the symmetry indices ISXCSF and ISYCSF in the CSF file These are analogous to the indices ISX and ISY in the body GDF file In most cases the same values must be used in the two files ISXCSF ISX and ISYCSF ISY Certain exceptions should be noted e If the CSF is defined by the user as described in Sections 11 2 and 11 3 below and if the intermediate free surface is not required as explained above a symmetric CSF can be used regardless of the body symmetries e If the CSF is defined by the user as described in Sections 11 3 and 11 4 below and if the body is submerged or in unusual cases where the body is not symmetric but the waterline is symmetric a symmetric CSF can be used regardless of the body symmetries If a control surface is defined with one or two planes of symmetry and the flow is not symmetric about these planes for example due to multiple body interactions the program reflects the control surface 11 2 LOW ORDER CONTROL SURFACE FILE In the low order method the control surface is represented by an ensemble of panels The CSF file contains a the vertex coordinates of the panels in the same format as in the GDF file The data in the CSF file is input in the following form header O CILOWHICSF ISXCSF ISYCSF NPAN
222. diffraction problem and if there are planes of symmetry only the symmet ric component of the diffraction potential is evaluated For this reason it is necessary to specify the complete diffraction solution IDIFF 1 to evaluate field data free surface elevation pressure and fluid velocity or to evaluate the drift forces A warning message is displayed in cases where the solution of the diffraction problem is incomplete 14 2 SOLUTION OF THE LINEAR SYSTEMS WAMIT includes three optional methods for solving the linear systems of equations in cluding a direct solver which is relatively robust but time consuming an iterative solver which for large systems of equations is much faster and a block iterative solver which com bines the advantages of each to some extent The parameter ISOLVE in the configuration file is used to select which method is used for the run With the default value ISOLVE 0 WAMIT solves the linear systems by means of a special iterative solver The maximum number of iterations is controlled by the parameter MAXITT in the configuration files See Section 4 7 with the default value equal to 35 If convergence is not archieved within this limit a warning message is issued and the computation continues without interruption If the number of iterations displayed in the output is equal to MAXITT this also indicates that convergence does not occur The time required for this method is proportional to NEQN times the number of
223. directory in this mode select the EE seo s Choose Setup Type Choose the setup ci best E E Typical Choose this option for complete typical install You will only define the install directory MultiSurf for WAMIT Users _ Choose this option if you will install MultiSurf for WAMIT You will only define the install directory Custom Allows users to choose which program features will be installed and where they will be installed Recommended for advanced users Figure 2 2 Installation mode selection window for both lease and site licenses 15 WAMITV7 Setup Destination Folder Click Next to install to the default folder or click Change to choose another Install WAMITV7 to C WAMITv7 Change aa Figure 2 3 Installation directory configuration window for both lease and site licenses The WAMIT software includes the main executable program wamit exe the DLL files listed below a complete set of input files for the standard test runs TESTn n 01 02 and the formatted output files TESTn OUT for these test runs The included text file readme txt includes an outline of the directory tree and files If any difficulties are encountered during installation and testing the user should confirm that the subdirectories and files correspond to the description in readme txt 2 3 115 WAMITv7 Setu n X Custom Setup eS Click the
224. dy 3 9 di 0 1 80665 17 21 44 OrFRN W N N NONNONODCONNNNN 15 1 2 0 6 1 2 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 test22b gdf ULEN GRAV ISX ISY NPATCH NLINES 4 5 4 2 XBOW XMID XAFT HBEAM HTRANSOM DRAFT DTRANSOM 2 IGDEF npatch 7 2 5 INONUMAP xbody 3 O 100000 100000 000000 100000 100000 100000 100000 000000 000000 100000 100000 000000 100000 100000 000000 100000 100000 000000 000000 000000 100000 100000 000000 100000 100000 100000 100000 000000 000000 100000 100000 000000 O NN OONN KDNNIOYNNONNOOONNONNONNOON NN NDNIDNONMNY 000000 000000 000000 100000 100000 000000 000000 100000 100000 100000 100000 100000 100000 100000 100000 000000 000000 000000 000000 000000 000000 000000 000000 100000 100000 O 000000 100000 100000 100000 100000 100000 100000 100000 000000 1 2 patch8 tanki fwd patch9 tanki side patchi0 patchil patchi2 patchi3 patchi4 patchi5 tank1 tanki tanki tank2 tank
225. e IGDEF 2 The geometry is defined by inputs from a MultiSurf ms2 file IGDEF lt 0 or gt 2 The geometry of each patch is represented explicitly by a special subroutine with optional data in the GDF file 7 7 7 5 GEOMETRY REPRESENTED BY LOW ORDER PANELS IGDEF 0 The simplest option to define the body geometry is appropriate if each patch of the body surface is a flat quadrilateral in physical space In this case the vertices of each patch are input via the GDF file in the same format as described in Section 6 1 for the low order method header ULEN GRAV ISX ISY NPATCH O X1 1 Y1 1 Z1 1 X2 1 Y2 1 Z2 1 X3 1 Y3 1 Z3 1 X4 1 Y4 1 Z4 1 X1 2 Y1 2 Z1 2 X2 2 Y2 2 Z2 2 X3 2 Y3 2 Z3 2 X4 2 Y4 2 Z4 2 X4 NPATCH Y4 NPATCH Z4 NPATCH The data in the first four lines are defined above in Section 7 4 Note that IGDEF 0 is assigned on line 4 The patch vertices X1 Y1 71 X4 Y4 Z4 are defined in precisely the same manner as the panel vertices in Section 6 1 The convention defined in Figure 6 1 must also be applied here with the vertices numbered in the anti clockwise direction when the patch is viewed from the fluid domain This option is particularly useful in the case of structures which consist of a small number of flat surfaces Examples include rectangular barges similar vessels with rectangular moonpools the Hibernia platform a star shaped bottom mounted cylinder etc In such cases it is
226. e 13 The cylinder extends from the free surface where it is free down to the bottom at a depth of 200m where it is clamped The cylinder radius is 10m Since the cylinder is clamped at the bottom the six rigid body modes are all fixed and specified by the values MODE j 0 in the POT file External mass and stiffness matrices are defined in the Alternative 2 FRC file The cylinder is considered to have a constant distributed mass equal to half of the displaced mass of fluid and also a concentrated mass at the free surface equal to the displaced mass The stiffness factor EJ for the beam equation is assumed constant with the value 0 41moh where mo is the concentrated mass and A is the fluid depth No matrix elements are required for the square submatrix i j lt 6 since the body is fixed in these modes Further details for this case are given in 13 The cylinder geometry is defined with two planes of symmetry and 512 panels on one quadrant The length scale ULEN is specified as 1 0 to simplify the definitions of modes and output quantities The generalized modes are defined in the subroutine defmod f which is distributed to licensed users The use of DEFMOD is described in Chapter 8 The output file from DEFMOD TEST08 MOD is included with the test files so that this test can be run without prior use of DEFMOD Only one wave period is considered here which coincides with resonant bending motion of the cylinder See also TEST18 where t
227. e see Section 4 7 e The configuration parameter TOLGAPWL can be used to adjust the tolerance for gaps between adjacent elements of the body waterline see Section 4 7 e The configuration parameter RAMGBMAX can be used to take maximum advantage of the computer s available RAM for storage of temporary scratch files Depending on the input parameters of the run and the hardware this can be used to achieve substantial savings in run time See Sections 4 7 and 14 3 e Version 7 0 is compiled with the Intel Fortran Compiler Version 12 1 using special directives to provide parallel processing on systems with multiple processors This can result in significant reductions of run times with a single processor and dramatic reductions with multiple processors See Section 14 6 e The separate Froude Krylov and scattering components of the exciting force and mo ment can be evaluated by using the extended options OPTN 2 3 2 See Sections 4 3 and 5 3 e Both configuration files config wam and cfg can be used to input the configuration parameters See Section 4 7 e New algorithms are used to evaluate the Rankine and log singularities in the low order method e The option IFORCE 2 can be used to run FORCE and POTEN in the same period loop and obtain portions of the numeric output files before the run is completed See Section 4 14 e The number of processors used and estimated RAM required for the run are output in the file wamitlog
228. e 7 can have other text following the required entries separated only by one or more spaces This additional data has no effect in Fortran and is likewise being ignored by C Line 7 is an exception because presence of a tank list on this line is optional if there is a second token on line 7 Fortran will try to interpret is as a tank list name Example GDF Tension leg platform example 120 32 2 ULEN GRAV 1 1 ISX ISY QO 2 NPATCH IGDEF 3 NLINES TLP4H MS2 wetted_surfs O 2 O Fast DivMult outward normals Explanation The first lineis an identifying message ULEN is 120 and GRAV is 32 2 This value of GRAV implies that the length unit for the global WA MIT model is feet If this MS2 file uses meters for its units conversion from meters to feet will be performed in RGKINIT The model has mirror symmetry with respect to its X and Y planes only one quadrant is explicitly modeled NPATCH is specified as 0 the interface will count the surfaces in Entity List wetted_surfs to determine N PATCH IGDEF is 2 to signify geometry from an M82 file 3 for N LIN ES indicates 3 lines to follow The MS2 fileis TLP4H MS2 This mode file must contain an Entity List named wetted_surfs which names the wetted surfaces This example has no tank list The last line specifies Fast evaluation a divisions multiplier of 2 overriding any divisions multiplier in the model file and the mode is constru
229. e Fourier transforms from the frequency domain to the time domain are evaluated in F2T by Filon numerical integration This method provides relatively accurate results for large values of the time variable t A fundamental requirement is that the frequency domain data must be evaluated by WAMIT for a large number N of uniformly spaced frequencies wn where n 1 2 3 N Special attention is necessary to ensure that the in crement Aw Wy41 Wn is sufficiently small to preserve the accuracy of the numeri cal integration and that the highest finite frequency wy is sufficiently large to span the physically significant range of frequencies for the application or from the mathematical standpoint to ensure that the truncated Fourier integrals are reasonable approximations of the infinite integrals In view of the need to include high frequencies in the WAMIT analysis it is usually advisable to use the irregular frequency option IRR 1 unless the body is submerged or its waterplane area is very small The requirement of accuracy over a broad range of frequencies means that either a large number of low order panels should be used or alternatively that the higher order method is used with appropriate control of the panel subdivision indices NU NV or the global parameter PANEL_SIZE Section 6 6 of Reference 26 contains additional information including an outline of the numerical method and comparisons with the results from the time domain panel progra
230. e data in this array are in pairs denoting the first and last index for each tank An even number of indices must be included on each line Each pair of tank indices must be enclosed in parentheses as shown in the input file test22 cfg More than one line can be used for multiple tanks and or multiple tanks can be defined on the same line Only integer data and parentheses are read for the array NPTANK with spaces or other characters separating each index Other ASCII characters may be used in addition to the integers and parenthesis but integers and parenthesis must be used only for the inputs above Note that all of the panels or patches defining the interior of a tank must be contiguous and specified by a single pair of indices since this is the way in which each separate tank is defined Further details and examples are given in Section 12 1 NUMHDR is the integer parameter used to control writing of a one line header in the numeric output files NUMHDR 0 No headers are included NUMHDR 1 A one line header is included in the numeric output files specifying the file name date and time The default value is NUMHDR 0 NUMNAM is the integer parameter used to control the assignment of filenames to the numeric output files NUMNAM 0 Numeric filenames are assigned based on the filename of the FRC input control file The same filename is used for the OUT output file NUMNAM 1 Numeric filenames are assigned as optn The defaul
231. e drift force and moment Option 8 The maximum number of integration ordinates in the azimuthal direction is 2MAXMITS The default value MAXMIT 8 is assigned unless a different value is input in the CFG file this value is recommended for general use MODLST is the integer parameter used to control the order in which the added mass and damping coefficients exciting forces and RAO s for different modes of motion are written to the output files MODLST 0 Outputs are in ascending order of the modal indices MODLST 1 Outputs are in the order evaluated for each of the corresponding left hand sides These two alternatives differ only if NLHS is greater than one The default value is MODLST 0 MONTTR is the integer parameter used to control the display of output to the monitor during the execution of FORCE MONITR 0 Outputs to the monitor are abbreviated consisting of the header text and displays of each wave period as it is executed This option is convenient in long runs of FORCE with extensive lines of output to permit monitoring the progress of the execution MONITR 1 Outputs of all data evaluated by FORCE are displayed on the monitor during execution in the same format as in the OUT file The default value is MONITR 0 NCPU is an integer which specifies the number of parallel processors CPU s also known as cores which are available on the system The default value NCPU 1 is applicable for most older PC s The use of
232. e fluid pressure velocity and free surface elevation The principal input files to the subprogram POTEN are the Potential Control File POT which specifies parameters including the fluid depth wave periods and wave heading angles and the Geometric Data File GDF which describes the geometry of the structure to be analyzed These files are discussed briefly below and in more detail in subsequent Chapters The principal input files to the subprogram FORCE are the Force Control File FRC which specifies inputs regarding the body dynamics and the P2F file Poten to Force which transfers data from POTEN to FORCE Three additional input files should also be used 1 Licensed users of WAMIT V7PC must utilize a unique input file userid wam which identifies the license 2 the optional input file fnames wam is recommended to specify the input filenames and 3 the configu ration files config wam and or cfg specify parameters and options which are required by the program Samples of the fnames wam and configuration files are included with the test runs for example the files test01 wam and test01 cfg are intended for use with TESTO1 By default in WAMIT the file fnames wam lists the filenames of the POT CFG and FRC files The GDF filenames are included in the POT file In Version 7 it is possible to use both the config wam and cfg files together as explained in Section 4 7 It is recommended to use config wam to specify inputs whi
233. e is not involved in the calculations Fast evaluation is usually much faster and always more predictable in terms of performance but involves some compromise of accuracy due to interpolation errors Our general experience is that with the default 8x4 divisions x subdivisions most curves and surfaces evaluate to near single precision accuracy under fast evaluation The accuracy should improve as the fourth power of the divisions provided the divisions on all supporting curves and surfaces are increased in constant proportion The divisions multiplier Tools Settings Performance tab is a simple way to make this increase uniformly across the model The GDF file format provides for overriding the model s divisions multiplier see below Pending further investigation of the accuracy of the integrated system our current recommendation is to use fast evaluation mode with default divisions and a divisions multiplier of 1 This should have little impact on performance and should provide WAMIT with full single precision accuracy for the geometry 4 9 Divisions and Subdivisions In MultiSurf each surface has division and subdivision properties that control how the surface is subdivided for tabulation and display For low order WAMIT panelizations we use the divisions x subdivisions to determine the mesh density and some care with divisions is often required to make neat watertight junctions between the panels on adjacent s
234. e nondimensional free surface elevation due to jth mode is defined by n Nj E Ln Pj where n 0 for j 1 2 3 and n 1 for j 4 5 6 The evaluation of the pressure or free surface elevation requires special caution close to the body surface Within a distance on the order of the dimensions of the adjacent panel s field point quantities cannot be computed reliably More specific limits can be ascertained by performing a sequence of computations and studying the continuity of the result Approaching the body along a line normal to the centroid of a panel will minimize this problem See Reference 12 regarding the computation of run up at the intersection of the body and free surface The parameter TOLFPTWL can be used to check for field points on the free surface which are close to or inside body waterlines see Section 4 3 3 7 3 7 VELOCITY VECTOR ON THE BODY AND IN THE FLUID DOMAIN The nondimensional velocities evaluated by WAMIT are defined in vector form by a V _ 6 V Vo KL VO igA wL Veo KL GVE j l where V iV is the nondimensional gradient operator These parameters can be evaluated separately for the diffraction or radiation problems by assigning the configuration parameters INUMOPT5 1 and or INUMOPT6 1 as ex plained in Section 4 7 The evaluation of the velocity requires special caution close to the body surface in the same manner as the pressure and free surface elevation When the radiation
235. e of the GDF file In the subroutine the depth of the axis is the same for all wavemaker elements The number of wavemakers is arbitrary but each separate mode of motion corresponds to one patch or panel of the geometry in the same order as these are defined in the gdf file In the low order method this effectively restricts the use of the subroutine to only one panel per wavemaker Thus it is strongly recommended to use the higher order method ILOWHI 1 when using the subroutine WAVEMAKER NEWMDS NPATCH must be specified in the pot or cfg file with the same value as the number of patches in the gdf file The subroutine WAVEMAKER includes two additional options specified by IGEN MDS 211 and IGENMDS 212 If IGENMDS 211 each wavemaker is like a piston with constant normal velocity on its surface If IGENMDS 212 a bank of contiguous wavemak ers are joined by vertical hinges and represented by tent functions with constant normal velocity in the vertical direction Further information is given in the header of this sub routine TEST23 described in Appendix A 23 illustrates the use of the option IGENMDS 21 for a bank of eight wavemakers along the wall x 0 with symmetry about both x 0 and y 0 The generated wave elevations for each wavemaker are evaluated over a square array of 8 x 8 64 field points The depth of the horizontal axis is specified by the parameter ZHINGE 2m in the input file test23_wmkrhinge dat 12 11 12 4 BODIES AN
236. e other three waterlines of the TLP The partition boundary is down along the y axis and then to the right along the x axis in accordance with the counter clockwise rule This example illustrates a useful feature that the outermost points do not need to intersect the outer boundary the program extends or reduces the first and last segments automatically to intersect the outer boundary the inputs 50 0 and 30 0 could be replaced by any positive numbers Figure 11 1 View from above the free surface showing four quadrants of the TLP control surface with a circular outer boundary The partition boundary is represented by the heavy dashed line as input in the CSF file shown above for Example 3 before it is extended by the program to intersect the outer boundary 11 13 Example 4 ten waterlines two and a half in each quadrant with rectangular outer bound ary as in TEST15 semi sub with a total of ten columns 1 ILOWHICSF 1 1 ISX ISY O O 10 NPATCSF ICDEF PSZCSF 0 0 40 0 RADIUS DEPTH 4 NPART 3 NV 1 150 0 0 0 150 0 60 0 0 0 60 0 end of partition 1 outer boundary of control surface 3 NV 2 0 0 0 0 30 0 0 0 30 0 50 0 end of partition 2 encloses middle half column 4 NV 3 30 0 50 0 30 0 0 0 90 0 0 0 90 0 50 0 end of partition 3 encloses second column 3 NV 4 90 0 50 0 90 0 0 0 150 0 0 0 end of partition 4 encloses third column In this case the first partition bounda
237. e user is interrogated with options to over write the old P2F file or to assign a different name to the new file This interruption can be avoided by renaming or deleting the old P2F file or using the configuration parameter IDELFILES as explained in Section 4 7 The P2F files can be relatively large depending on the parameters of the run Unless future use is anticipated it may be best to erase or over write old files Chapter 6 THE LOW ORDER METHOD ILOWHI 0 This Chapter includes specific topics which are applicable when the low order method is used as in earlier versions of WAMIT The essential features of this method are a the geometry of the body is represented by an ensemble of flat quadrilateral panels or facets and b the solutions for the velocity potential and optionally for the source strength are approximated by piecewise constant values on each panel The geometry of the body is specified in this case by a Geometric Data File GDF which includes the Cartesian coordinates of each vertex of each panel listed sequentially In addition the GDF file specifies the characteristic length ULEN used for nondimensional ization of outputs the value of the gravitational acceleration constant GRAV in the same units of measurement the number of panels NPAN and two symmetry indices ISX ISY as described in Section 6 1 The syntax for data in this file follows the same requirements outlined for the generic input files in Chapter 4
238. eak wam The file break wam can be established either before execution of WAMIT or during the run To establish the file during runtime in the PC environment it is necessary either to use a second DOS Command Prompt window or to establish the file using a Windows Edit command When multiple processors are used NCPU gt 1 the break wam file is ignored and it is not possible to interrupt the execution of POTEN until the loop over all wave periods is completed 4 13 ASSIGNING RAO S IN AN EXTERNAL FILE It is possible to input RAO s from an external file referred to as the external RAO file This permits users to modify RAO s to take into account physical effects which are not included in the original WAMIT computations and to evaluate other hydrodynamic pa rameters including the drift forces pressures and velocities based on the modified values of the RAO s This option is controlled by the parameter IREADRAO in the CFG file as explained in Section 4 7 If IREADRAO 0 default the RAO s computed by WAMIT in Option 4 are used to evaluate the other hydrodynamic parameters Options 5 9 In a typical application where the RAO s are to be modified two separate WAMIT runs are executed These are summarized in the two following paragraphs If IREADRAO 1 is assigned in the CFG file the WAMIT run is executed in the same manner as in the default case except that Options 5 9 are not evaluated The results are the same as if IOPTN 5 9
239. ed Bernoulli equation E Poa The total velocity potential is defined by 6 p pp iw Esp j 1 where the radiation and diffraction velocity potentials are defined in Section 15 1 The nondimensional velocity potential and hydrodynamic pressure are defined as follows 6 Pp _ as p 7 Gpt KL Ej Pi Pg j l where K w g and YD oS Pj igA w 1 pm with n 0 for j 1 2 3 and n 1 for j 4 5 6 The body pressure can be evaluated separately for the diffraction or radiation prob lems by assigning the configuration parameters INUMOPT5 1 and or INUMOPT6 1 as explained in Section 4 7 When the radiation components are output separately the nondimensional pressure due to jth mode is defined by pags Special definitions are required in the limits of zero and infinite wave periods as ex plained in Section 3 9 3 6 3 6 FREE SURFACE ELEVATION The free surface elevation is obtained from the dynamic free surface condition __1 a i g t and in nondimensional form 6 n o i 45 ev KEYG Iz z 0 where is defined as in Section 3 5 The nondimensional hydrodynamic pressure and wave elevation are equal to the nondimensional velocity potential at the respective positions These parameters can be evaluated separately for the diffraction or radiation prob lems by assigning the configuration parameter INUMOPT6 1 as explained in Section 4 7 When the radiation components are output separately th
240. ed by a tensor product of B spline basis functions olu v 5 5 bigUi w Vj v 7 4 Here U u and V v are the B spline basis functions of u and v and M and M are the number of basis functions in u and v respectively The unknown coefficients Q are determined ultimately by substituting this representation in the integral equation for the 7 5 potential as described in Chapter 15 The total number of unknowns on a patch is M x M In the low order panel method the accuracy of the numerical solution depends on the number of panels To a lesser extent the panel arrangement such as cosine spacing may also affect the accuracy of the solution In the higher order method the accuracy depends on two parameters the order of the basis functions and their number M and M Order is defined as the degree of the polynomial plus one For example a quadratic polynomial u au b is of order three We denote the order of U u and V v by K and Ky respectively Further information regarding the B spline basis functions can be found in Reference 22 While K and K are input parameters specified by users M and M are not direct input parameters to WAMIT Instead users may specify the number of panel subdivisions on each patch N and N In standard B spline terminology these correspond to knots Alternatively users can specify the desired size of each panel in physical space and the program will automatically assign the correspo
241. ed for the options described in Sections 7 5 7 7 and thus IGDEF gt 3 or IGDEF lt 1 are appropriate values to select for the analytic representation option In the WAMIT software package as distributed several negative values IGDEF lt 1 have been used for the test runs and for other pertinent examples which may be useful Thus it is recommended that any new additions to this library developed by users should be identified with positive values IGDEF gt 3 Continuing with the example of the circular cylinder shown in Figures 7 1 and 7 2 the subroutine CIRCYL can be used without modification CIRCYL is included in the source file GEOMXACT F and selected by specifying IGDEF 1 The relevant dimensions are the radius and draft and also ULEN and GRAV which are specified in the GDF file in the following format header ULEN GRAV 1 i 2 2 RADIUS DRAFT INONUMAP Here the symmetry indices ISX 1 and ISY 1 have been assigned as well as the parameters NPATCH 2 and IGDEF 1 The number 2 on line 5 indicates that two lines follow in the file to be read as input data In addition to the dimensions of the cylinder the parameter INONUMAP is used in subroutine CIRCYL to specify either uniform INONUMAP 0 or nonuniform INONUMAP 1 mapping between the parametric coordinates U V and the Cartesian coordinates X Y Z Uniform mapping uses linear functions to transform V to the vertical coordinate on the side and to the radial coordinate
242. ed from the nondimensional inertia matrix 5 10 THE INTERMEDIATE DATA TRANSFER FILE P2F The file pot p2f is written by POTEN and read by FORCE The filename pot is the same as the POT input file The P2F file contains the solutions of the linear systems of equations for the velocity potential and source strength on the body surface and also some inputs to POTEN which are required by FORCE e g the wave periods and heading angles specified in the POT file To facilitate data transfer the P2F file is a binary file and it cannot be used for purposes other than as input to FORCE The P2F file can be used for multiple runs of FORCE in situations where the outputs from POTEN are the same TEST17b is an example of this situation where the only change from TEST17a is to apply an external damping force on the lid to attenuate the moonpool resonance See Section A 17 In this case IPOTEN 0 is assigned in the configuration file and the POTEN run is skipped with considerable savings of time Increasing the number of Haskind wave heading angles adding options in FRC which were omitted in the original run and using an external RAO file Section 4 13 are examples of other situations where it is useful to save the original P2F file and avoid the extra computational time required to repeat the POTEN run If another run is made using the same POT file with IPOTEN 1 default and with an old P2F file in the same directory with the same filename th
243. ed to give a more accurate plot IPLTDAT 5 is used for the plots shown in Sections A 11 19 In the higher order method ILOWHI 1 the optional output file gdf LOW GDF is controlled by the integer parameter ILOWGDF in the configuration files If ILOWGDF gt 0 a low order GDF file is generated using the panel vertices of the higher order geometry with ILOWGDFxILOWGDF sub divisions The first three lines are copied from the higher order GDF input file The total number of sub divided panels is included on line 4 This option can be used to generate low order GDF files for any of the geometries which can be input to the higher order method including geometries represented by a small number of flat patches Section 7 5 B splines Section 7 6 and geometries which are defined in the subroutine GEOMXACT Section 7 8 In each case the number of low order panels can be increased by increasing the value of ILOWGDF The coordinates of the panels are in the same body fixed dimensional system as the original input data These optional files are generated in the POTEN subprogram after reading the geom etry input files and before looping over the wave periods If NPER 0 these files can be generated quickly without the extra time required to solve for the potential and hydrody namic parameters 5 8 ERROR MESSAGES Numerous checks are made in WAMIT for consistency of the input data Appropriate error messages are displayed on the monitor to assist in cor
244. ed to mean that the water depth is infinite It is recommended to set HBOT 1 in this case If HBOT is positive it must be within the range of values 10 lt HBOT x w a 10 where w is the radian frequency of the incident waves and g GRAV is the gravitational 4 7 acceleration constant For each run the value of GRAV is input in the GDF file as described in Chapters 6 and 7 All dimensional inputs with the units of length including HBOT must be consistent with the input GRAV Typically either GRAV 9 80665 is used for the metric system or GRAV 32 174 is used if the length scale is in feet IRAD IDIFF are indices used to specify the components of the radiation and diffraction problems to be solved The following options are available depending on the values of IRAD and IDIFF IRAD 1 Solve for the radiation velocity potentials due to all six rigid body modes of motion IRAD 0 Solve the radiation problem only for those modes of motion specified by setting the elements of the array MODE I 1 see below IRAD 1 Do not solve any component of the radiation problem IDIFF 1 Solve for all diffraction components i e the complete diffraction problem IDIFF 0 Solve only for the diffraction problem component s required to evaluate the exciting forces in the modes specified by MODE I 1 IDIFF 1 Do not solve the diffraction problem NPER is the number of wave periods to be analyzed NPER must be an integer The follow
245. een the generalized and rigid body modes should be included The gravitational force and moment associated with the rigid body modes i 7 lt 6 should not be included since these components are evaluated in the program It is not possible for the program to evaluate the hydrostatic matrix in a unique manner which applies to all possible situations including the effects of the gravitational force associated with the internal mass of the body The coefficients evaluated and used by the program are specifically those defined by the matrix of hydrostatic and gravitational restoring coefficients listed in Section 3 1 for the rigid body modes and by the hydrostatic matrix 9 12 for the generalized modes Users should input additional restoring coefficients as necessary using the EXSTIF matrix 9 9 9 5 NBODY ANALYSIS The NBODY and generalized mode analyzes can be combined An example where this might be effective is if two separate bodies are in close proximity one or both of them are undergoing structural deflections and there are no planes of geometric symmetry for the ensemble of two bodies If NBODY gt 1 separate values of NEWMDS and IGENMDS must be specified for each body Both parameters are defined in the configuration file using separate lines for each body with the syntax NEWMDS m n IGENMDS m i Here m is the body index n is the number of new modes for that body and 7 is the value of IGENMDS appropriate for the same
246. eling technique in MultiSurf Comparison of the results with TEST11b indicates that they are practically identical Input file testil cfg TEST11 CFG Cylinder R 1 T 0 5 igdef 1 ipltdat 5 ilowgdf 5 ILOWHI 1 IRR 0 ISOLVE 2 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NOOUT 111101111 NUMHDR 1 Input file testil pot TEST11 POT Cylinder R 1 T 0 5 igdef 1 i 1 1 IRAD IDIFF 3 NPER array PER follows 8 971402 2 006403 1 003033 1 NBETA array BETA follows O 1 NBODY test11 gdf 0 0 0 0 XBODY 11 1 1 1 1 IMODE 1 6 First 10 lines of input file testil gdf TEST11 cylinder R 1 T 0 5 defined by B splines IGDEF 1 1 9 80665 ULEN GRAV 1 1 ISX ISY 2 1 NPATCH IGDEF 4 2 4 4 1 00000000000000 1 00000000000000 1 00000000000000 1 00000000000000 0 500000000000000 O 000000000000000E 000 O 500000000000000 1 00000000000000 1 00000000000000 1 00000000000000 1 00000000000000 Input file test11 spl TEST11 cylinder R 1 T 0 5 defined by B splines IGDEF 1 4 2 NU NV Patch 1 side u azimuthal v vertical 4 2 NU NV Parch 2 bottom u azimuthal v radial Input file testil frc TEST11 FRC Cylinder R 1 T 0 5 igdef 1 1 1 1 14 3 3 0 2 2 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 50 O 1 5 0 0 5 end of file Input file testila cfg TEST11a CFG Cylinder R 1 T 0 5 igdef 1 ipltdat 5 ILOWHI 1 IRR 0 ISOLVE
247. en Option 7 is used as described in Chapter 11 the control surface should include the free surface exterior to the body if this is necessary and should not include the FSP surfaces 12 16 12 6 INTEGRATING PRESSURE ON PART OF BODIES Starting in Version 7 1 the cfg parameter NPFORCE or NPNOFORCE can be used to include or omit specified panels or patches in the integrations of the pressure force and moment on the body surface This option can be used for example to evaluate structural sheer loads on elongated bodies If NPFORCE is included in the cfg inputs as described in Section 4 7 only the panels or patches specified are included in the integrations Conversely if NPNOFORCE is included in the cfg inputs these panels or patches are omitted from the integrations These two parameters are complementary and cannot be used together for the same body If both parameters are included in the cfg inputs an error message is generated and the program stops unless they are assigned with different body indices see Section 8 4 The forces computed with NPFORCE or NPNOFORCE can also be evaluated using generalized modes as described in Chapter 9 with the mode shapes equivalent to the rigid body motions only on the panels or patches specified by NPFORCE or only on the panels or patches which are not specified by NPNOFORCE The use of NPFORCE or NPNOFORCE is simpler than the use of generalized modes since it is not necessary to define the modes requi
248. en the body shape is relatively complex and the latter KSPLIN 4 when the body is smooth and continuous e g a sphere Most of the test runs described in the Appendix use KSPLIN 3 Experience also suggests that efficient choices for the inner and outer Gauss integrations are equal to KSPLIN 1 and KSPLIN respectively Tests for accuracy and convergence can be achieved most easily and effectively by increasing the numbers of panels either by increasing NU and NV or by decreasing the parameter PANEL_SIZE This procedure permits systematic convergence tests to be made easily and efficiently without simultaneously changing the other parameters or inputs 7 12 THE USE OF DEFAULT VALUES TO SIMPLIFY IN PUTS Experience with the higher order method indicates that for typical applications the global parameters defined above may be assigned the values KSPLIN 3 IQUADO 3 IQUADI 4 These default values are assigned by the program automatically if they are not assigned in the configuration files and if there is no SPL input file available to open and read with the same filename as the GDF file In the latter case however the parameter PANEL_SIZE must be specified with a nonzero positive value in CONFIG WAM This is the simplest way to use the higher order method since it does not require the user to input the B spline and Gauss quadrature orders either locally in the SPL file or globally in the CONFIG WAM file The following table summarizes the options
249. ename and to edit the fnames wam file to show the corresponding new filename for the force control file If this procedure is followed the output file will carry the same filename with the out extension to distinguish it from the original file test01 out The user may then compare the RAO s in the different output files to discern the effect of these changes As the second modification WAMIT may be re run with a more extensive list of wave periods Edit the potential control file test01 pot with the following changes e on line 5 change the number of wave periods NPER from 3 to 10 e on line 6 replace the three original wave periods by ten new periods in decimal format e depending on your preference 1 save the modified file with the original name test01 pot or 2 save the modified file with a new filename and correct the fnames wam file on line 2 with this new filename Since it is necessary to re run POTEN in this case delete the line IROTEN 0 if this was added to test01 cfg During the run if the original filename test01 p2f is retained the user will be prompted whether or not to overwrite the old output file test01 p2f overwriting is the simplest procedure to follow in this circumstance otherwise the new P2F filename must be specified before the FORCE run is executed The input files for other test runs can be used to illustrate various options and modifi cations Chapter 3 DEFINITION OF QUANTITIES EVALUATED BY WAM
250. entation of the geometry can be developed using the CAD environment of MultiSurf and b this representation can be transferred to WAMIT without significant effort or approximations Two special dll files are required RGKERNEL DLL and RG2WAMIT DLL The real versions of these files are not included in the standard WAMIT license Users who intend to use this option may license RGKERNEL and RG2WAMIT as part of an extended version of WAMIT or separately The standard distribution of WAMIT includes a dummy file with the name rg2wamit dll This enables WAMIT to be executed without the real files As explained in Section 2 1 the PC executable version of WAMIT wamit exe must be accompanied by eight dll files The dummy version of rg2wamit dll can be distin guished from the real version in two ways a the dummy filename uses lower case letters rg2wamit dll and b the size of this file is smaller as indicated in the following table version name size dummy rg2wamit dll 7Kb real RG2WAMIT DLL 233Kb The size of these files is approximate and may change with updates and subsequent ver sions but the disparity in size will serve to distinguish the dummy and real files To proceed with this option a user should first prepare the MultiSurf model for the body following the procedure in the MultiSurf documentation A special appendix Using the WAMIT RGKernel Interface is included in this User Manual Appendix C The o
251. ential can be evaluated either in a similar manner as for the Rankine source or together with the regular part of the wave source potential The parameter ILOG in the configuration files controls these options When ILOG 1 the logarithmic singularity is subtracted from the wave source potential and integrated separately When ILOG 0 it is included in the evaluation of the wave source potential and integrated by the same quadrature 15 6 REMOVAL OF IRREGULAR FREQUENCIES The irregular frequency effects are removed from the velocity potential and the source strength using the extended boundary integral equations The details of discussion on the method are provided in Reference 8 and 16 The extended boundary integral equation for the potential formulation 15 11 takes a form 2mp x ff d IGE e 4 ah i 96066 ap a Sg d xE 15 42 15 9 inate ff p0 Ses Ihe Ez o EG EdE xeS 15 43 Here y x is the unknown velocity potential on the body surface S and y x is the nonphysical velocity potential on the interior free surface S The corresponding equations for the source formulation 15 26 are 2mo x Go ff oE DE Gus ff o oe Dag WE xe S 15 44 4ro x ffo oe 06666 ae f oe oe O dt E xe S 15 45 15 7 INTEGRAL EQUATIONS FOR BODIES WITH THIN SUB MERGED ELEMENTS Green s integral equations in Section 15 2 become singular as the thickness of the body or part of the body de
252. entified as N 1 If the original body panels are reflected by the program the file gdf LOW GDF will include panels for the reflected body This will occur if NBODY gt 1 if walls are present or if the body is not symmetric with respect to the global coordinate system If ILOWGDF 1 and the body is reflected by the program gdf_low gdf contains the original body panels without subdivision plus their images about the reflected planes of symmetry The data in gdf_pan dat and gdf_pat dat are defined with respect to the global coordi nate system In a WAMIT run with NBODY gt 1 the data for all of the bodies are included The figures in Sections A 5 and A 13 illustrate this feature These files are described separately below for the low order and higher order methods In the low order method ILOWHI 0 the vertex coordinates of the body panels are stored in the output file gdf_pan dat using the Tecplot finite element format FEPOINT The integer parameter IPLTDAT in the configuration files is used to specify whether or 5 10 not to generate this output file In the default case IPLTDAT 0 no file is generated If IPLTDAT gt 0 the file is generated In the low order method ILOWHI 0 the optional output file gdf LOW GDF is con trolled by the integer parameter ILOWGDF in the configuration files If ILOWGDF gt 0 the output file gdf LOW GDF is generated with all of the original panels subdivided into ILOWGDFxILOWGDF sub divisions The first th
253. ents in each array is the product of these three integers X1 Y1 Z1 are the coordinates of the first point in the array DELX DELY DELZ are the distances between adjacent points in the array in each direction If NFX 1 indicating that there is only one point in the direction parallel to the x axis the value of DELX is irrelevant but must be assigned to prevent a read error Similarly for NFY 1 and or NFZ 1 the values of DELY and or DELZ are irrelevant The field points assigned using this procedure are augmented to the list of field points if any assigned in the conventional manner as explained inSection 4 3 If the array option is used for all field points then NFIELD 0 must be assigned At runtime NFIELD is increased to include all field points The complete list of all field points is output in the FPT file Test23 illustrates the use of this option 4 12 USING THE OPTIONAL FILE BREAK WAM In most cases the principal computational time required in WAMIT runs is in POTEN to set up and solve the linear system of equations for the velocity potential at each wave period This starts with the first wave period JPER 1 and continues in sequence to the last period JPER NPER where NPER is the number of wave periods specified in the POT file When the computations are completed for each wave period a one line display is shown on the monitor including the wave period clock time and numbers of iterations for the radiation and diff
254. er TOLGAPWL can be modified if necessary to define the allowable gaps between adjacent patches on the waterline Two alternative mappings are used to relate the Cartesian body coordinates x y and parametric coordinates u v depending on the shape of the waterline along the outer edge of the patch If the slope of this waterline segment changes sufficiently greater than 5 radians over half of the segment a polar mapping is used Otherwise a ruled mapping is used spanning the half width between the axis and the waterline When ruled mapping is used the axis must be parallel to the plane y 0 as in the conventional choice of coordinates of ship like hulls Thus when such bodies are to be analyzed the longitudinal axis of the body should be parallel to the x axis In general there is one interior patch for each exterior waterline patch However if one or both ends of the waterline are straight lines within 0 1 radians of being perpendicular to the mapping axis this segment is defined as the side v 1 or v 1 of the adjacent interior patch Various examples of interior patches and panels are shown in Figure 10 2 corresponding to several of the standard test runs in the Appendix When the interior free surface patches are defined by the program the spline control parameters assigned for each patch are the same as those input for the associated exter nal patch except that the parameter NU is increased or decreased based on the relative widths
255. er and low order methods 7 2 7 1 SUBDIVISION OF THE BODY SURFACE IN PATCHES AND PANELS The body surface is first defined by one or more patches each of which is a smooth continuous surface in space Contiguous patches meet at a common edge where the coor dinates are continuous but the slope may be discontinuous A simple illustrative example is provided by the circular cylinder of finite draft shown in Figure 7 1 The same cylinder is shown in Figure 6 1 as it would be represented by low order panels Since there are two planes of geometric symmetry we consider only one quadrant represented by the shaded portion of Figure 7 1 Two patches are used one for the flat horizontal bottom and the other for the curved cylindrical side The important properties of the patches are that a the surface is smooth with continuous coordinates and slope on each patch and b the ensemble of all patches represents the complete body surface or one half or quarter of that surface if one or two planes of symmetry exist Figure 7 1 Representation of the circular cylinder by two patches on one quadrant shown by the shaded portion with reflections about the two planes of symmetry 7 3 On each patch a pair of parametric coordinates u v are used to define the position The parametric coordinates are normalized so that they vary between 1 on the patch Continuing with the example in Figure 7 1 denoting the cylinder radius R and the draft
256. ere to include problems where part or all of the body surface is one or more free surfaces and a nonzero oscillatory pressure acts on these surfaces On each of these surfaces the hydrostatic pressure is assumed constant and non negative Thus the surface is in a horizontal plane at z lt 0 The oscillatory component of the pressure is defined as the real part of po x y e The complete boundary surface Sp Sw Sp includes the wetted surface Sy and the pressure surface Sp To simplify the notation it is assumed here that NBODY 1 and there are no generalized modes The Neumann boundary conditions 15 9 and 15 10 are applicable on Sw and the boundary condition on Sp is Tw Pz Kp pola y 15 69 Pg It is convenient to represent the pressure distribution by 6 Mp polz y pg gt amp nj z y 15 70 j 7 where for j gt 6 is a normalized coefficient with the dimension of length and n is a nondimensional real function of position which represents the spatial dependence of the corresponding pressure mode The number of modes M required to represent the pressure distribution will depend on the application The total potential is given by 15 6 with the radiation potential extended in the form 6 M Pr iw 5 Eip 15 71 j 1 If the functions n are extended to apply on both S and Sp with the definitions n j 0 on Sw j gt 6 15 19 n j 0 on Sp 7546 the boundary conditions 15 9 and 15 6
257. erence to equations 15 2 and 15 4 the incident wave elevation at X Y 0 is equal to Re Ae A cos wt 3 2 If 6 gt 0 the output leads the phase of the incident wave and if 6 lt 0 the output lags the incident wave For field data pressure velocity and free surface elevation and mean drift forces the definitions given below in Sections 3 5 3 8 apply to the complete solution for the combined 3 1 radiation and diffraction problems The components of the field data can be evaluated sep arately for either the radiation or diffraction problems using the configuration parameters INUMOPT5 and INUMOP T6 as explained in Sections 4 7 and 5 2 For the sake of simplicity the definitions which follow in this Section assume that the origin of the body coordinate system is located on the free surface Special definitions apply to some quantities if vertical walls are defined as explained in Section 12 4 3 2 3 1 HYDROSTATIC DATA All hydrostatic data can be expressed in the form of surface integrals over the mean body wetted surface Sp by virtue of Gauss divergence theorem v ff meas ff nuds ff mas All three forms of the volume are evaluated in WAMIT as independent checks of the panel coordinates and printed in the summary header of the output file where they are denoted by VOLX VOLY VOLZ respectively The median volume of the three volumes is used for the internal computations If it is less than 102 a w
258. erline must obey the rule that as one progresses in the positive direction from one vertex to the next one passes around the waterline in a counter clockwise direction as viewed from above the free surface e When multiple waterlines are defined by the GDF inputs the order of the waterlines and the order of the partitions must correspond with the same number of each For example in TEST15 the columns of the semi sub are defined starting at the midship section X 0 and moving out toward the bow following the patch definitions of the subroutine SEMISUB in GEOMXACT in this case the partitions in the CSF file must follow the same order as shown in Example 4 below A proper sequence of the patches and panels must be followed in the GDF file and geometry definition all indices of the patches or panels belonging to each waterline must be either smaller or larger than all indices of the patches or panels belonging to the other waterlines The order of these indices defines the order of the waterlines and the partitions defined in the CSF file must follow the same order e When partitions are used to separate multiple waterlines the program will extend or contract the outer ends of the partitions so that they are located at the intersections with the outer boundary Thus as shown in Figures 11 1 and 11 2 it is not neces sary for the user to compute the exact coordinates of the intersections In these two Figures the coordinates of the intersections a
259. ernative inputs are equivalent for the case NBODY 8 to illustrate this rule in a situation where IALTFRC is not the same for all bodies IALTFRCN 2 1 2 2 2 2 2 2 IALTFRCN 2 1 2 Different values of the irregular frequency parameter IRR can be assigned for each body as indicated in the example above by including the body index in parenthesis Alternatively the same value of IRR can be input for all bodies See Section 10 5 The parameter NPTANK identifies the internal tanks which are associated with the corresponding body Thus the input NPTANK 1 defines the tanks to be in body 1 The 8 7 associated inputs RHOTANK and ZTANK are identified by the number of each tank and not by the body number The number of each tank is defined by the order of the inputs NPTANK in the configuration files The parameters NPFORCE and NPNOFORCE can both be included in the example above since they refer to different bodies See Section 4 7 and Section 12 6 8 8 8 5 GLOBAL SYMMETRY INDICES The geometric symmetry of each body is defined by the symmetry indices ISX ISY in the corresponding GDF file as explained in Sections 6 1 and 7 4 In solving the hydrodynamic problem for multiple bodies including body interactions it is necessary to consider the global symmetry which is affected by the position and orientation of each body Global symmetry exists only in cases where the combination of all bodies is symmetric about one or both planes In WAMIT V
260. eroid 0 5 meters and the origin of the global coordinate system is located at the mid point of this gap The relative locations of the two bodies and the orientation of the spheroid are specified in the GGDF file One quadrant of the cylinder is discretized with 112 panels 8 6 and 8 panels are distributed in the azimuthal radial and vertical directions using cosine spacing in radial and vertical directions One quadrant of the spheroid is discretized with 64 panels 8 and 8 panels are distributed in the longitudinal and transverse directions using cosine spacing in the longitudinal direction The Alternative 3 input format is used for FORCE The separate FRC files TESTO05C TESTOSS are used with IALTFRC 3 The vector IALTFRCN is included in TEST05 CFG to indicate that IALTFRC 1 in the separate FRC files for each body The added mass and damping coefficients exciting forces motions wave elevations field pressures and field velocities and drift forces are evaluated in infinite water depth for two wave periods and one wave heading The option is used to evaluate the mean drift force and moment using a control sur face following the instructions in Chapter 11 The control surfaces surrounding the cylin der and spheroid are defined by the input files TEST05c csf and TESTOSs csf In order to illustrate the alternatives the control surface for the cylinder uses low order panels ILOWHICSF 0 and the control surface for the spheroid is generated
261. ersion 6 it was assumed for NBODY gt 1 that there are no planes of global symmetry If one or more bodies are defined with planes of symmetry the geometric inputs for these bodies are reflected about the original planes of symmetry by the program to provide a complete description of the entire surface Starting in Version 7 0 global symmetry can be used to reduce the computational time in special cases where the body symmetries and their orientations are suitable These cases are described below In all other cases as in prior Versions the global symmetry indices are set to 0 0 when NBODY gt 1 When reflection of the original body geometry is required this is performed by the program We define ISG i as the vector of the global indices i 1 2 and ISB i n as the vector of body symmetries for each body n 1 2 NBODY XBODY j n is the array specifying the global coordinates of the origin of each body j 1 2 3 and its rotation j 4 about the vertical axis as explained in Section 4 2 The following rules are applied to determine the global symmetry indices e If XBODY 4 n is nonzero for any body ISG 0 0 e If ISB 1 n 1 and XBODY 1 n 0 and XBODY 4 n 0 for all bodies ISG 1 1 e If ISB 2 n 1 and XBODY 2 n 0 and XBODY 4 n 0 for all bodies ISG 2 1 To illustrate these rules Test05 in Appendix A includes a cylinder and spheroid both with two planes of geometric symmetry and located at different positions on the global x axis
262. ery large A brief outline for the theoretical basis of WAMIT is presented in Chapter 15 Reference 26 contains a more complete review of the pertinent theory A list of relevant references is included after the final chapter Appendix A includes de scriptions of the standard test runs Appendix B documents the use of the utility v6v7inp for converting Version 6 input files Appendix C describes the use of the interface between WAMIT and the MultiSurf kernel 1 1 WAMIT Version 7 WAMIT is a radiation diffraction program developed for the analysis of the interaction of surface waves with offshore structures WAMIT is based on a three dimensional panel method following the theory which is outlined in Chapter 15 The water depth can be infinite or finite Either one or multiple interacting bodies can be analyzed The bodies may be located on the free surface submerged or mounted on the sea bottom A variety of options permit the dynamic analysis of bodies which are freely floating restrained or fixed in position In addition to the conventional case where the bodies are rigid and moving with six modes of rigid body motion WAMIT permits the analysis of generalized modes to represent structural deflections motions of hinged vessels devices for wave energy conversion etc Part or all of the boundary surface can be defined as a free surface with an oscillatory pressure as in the case of an air cushion vehicle or oscillating water column
263. es The use of IOPTN 4 1 2 or 3 is explained in Section 4 5 IOPTN 5 IOPTN 5 0 do not output pressure and fluid velocity on the body IOPTN 5 1 output pressure on the body IOPTN 5 2 output fluid velocity on the body 4 13 IOPTN 5 3 output both pressure and fluid velocity on the body IOPTN 6 IOPTN 6 0 do not output pressure or velocity in the fluid and or free surface elevation IOPTN 6 1 output pressure in the fluid and or free surface elevation by the poten tial formulation IOPTN 6 1 output pressure in the fluid and or free surface elevation by the source formulation IOPTN IOPTN IOPTN 6 3 output both pressure and velocity in the fluid and or free surface elevation by the potential formulation 6 2 output velocity in the fluid by the potential formulation 6 2 output velocity in the fluid by the source formulation IOPTN 6 3 output both pressure and velocity in the fluid and or free surface elevation by the source formulation IOPTN 7 IOPTN 7 0 do not output the mean force and moment from control surface inte gration IOPTN 7 1 output the mean force and moment from control surface integration only for unidirectional waves IOPTN 7 2 output the mean force and moment from control surface integration for all combinations of wave headings IOPTN 8 IOPTN 8 0 do not output the mean force and moment from momentum integration IOPTN 8 1 output
264. es are displayed on the monitor during the run and in the log file wamitlog txt Since some of these messages may be lost on the monitor due to scrolling of other outputs a special warning message is generated at the end of the run to alert users when significant messages are contained in these two files Two particular warning messages which occur relatively frequently are the following e Number of subdivisions exceeds MAXSQR e WARNING no convergence in momentum Dx Dy Mz for headings When a warning message occurs indicating that the Number of subdivisions exceeds MAXSQR for the Rankine integration over a higher order panel the Cartesian coordinates of the field point and source point are output to wamitlog txt so that the user can more easily check if there is a singularity or inconsistency in the geometry definition in the vicinity of these points Usually this indicates either an error in the geometry definition or specification of a field point too close to the body surface The convergence test for the momentum drift force and moment is used to ensure ac curate integration of the momentum flux in the far field This integration is performed recursively increasing the number of azimuthal integration points by factors of 2 Conver gence is achieved when the difference between two successive iterations in each of the three components Dx Dy Mz is less than a prescribed tolerance TOL 10 If the component is less th
265. essure modes are used to represent anti symmetric and symmetric pressure distributions with constant pressure in each chamber denoted by Modes 7 and 8 respectively These pressure modes are defined by the NEWMODES subroutine PRESSURE_FS The configuration parameter ICCFSP 1 is used to include the external restoring coefficients due to the pressure acting on the upper surface of the air chambers see Section 12 5 Input file test25 cfg TEST25 CFG ACV air cushion vehicle with 2 air chambers ipltdat 1 ILOWHI 1 IALTFRC 1 ISOLVE 1 PANEL SIZE 1 0 NUMHDR 1 IMODESFSP 1 NMODESFSP 2 NPFSP 9 9 ICCFSP 1 Input file test25 pot use default spl parameters use NEWMODES subroutine PRESSURE_FS 2 pressure modes sym amp antisym about x 0 free surface pressure on patch 9 include external restoring coefficients TEST25 ACV air cushion vehicle with 2 air chambers 0 1 6 IRAD IDIFF NPER array PER follows 5 0 6 0 7 0 8 0 9 0 10 0 1 180 1 test25 gdf 0 0 0 0 1 0O 1 0O 1 0 NBETA array BETA follows NBODY XBODY IMODE 1 6 First 10 lines of input file test25 gdf TEST25 ACV air cushion vehicle with 2 air chambers igdef 0 1 00 1 9 9 00 9 00 10 00 10 00 9 00 0 00 9 80665 anon an 00 00 00 00 00 00 NPATCH IGDEF 2 00 2 00 0 00 0 00 end 2 00 2 00 Input file test25 frc TEST25 FRC ACV air cushion vehicle with 2 air chambers 1 1 1 1 0 o
266. etailed information in References 8 16 and 26 In this method the computational domain includes the interior free surface of the body and it is necessary to discretize both the body surface and the interior free surface The integer parameter IRR controls the removal of the effect of irregular frequencies Depending on the value of IRR the discretization of the interior free surface may be provided by the user or it may be done automatically by the program Explanation of the parameter IRR and the discretization of the interior free surface are given in the following Sections 10 1 INPUT PARAMETERS The parameter IRR is specified in the the configuration file as described in Section 4 7 with the default value zero The definition of IRR is as follows IRR is the integer used to specify whether the effect of the irregular frequency is removed or not The values IRR 0 1 2 3 can be used in the low order method ILOWHI 0 Only the values IRR 0 1 3 can be used in the higher order method ILOWHI 1 The definitions of each value are listed below with details given in the following sections IRR 0 Do not remove the effect of the irregular frequencies IRR 1 Remove the effect of the irregular frequencies The geometrical description of the interior free surface is included in the GDF file IRR gt 1 Remove the effect of the irregular frequencies The geometrical description of the interior free surface is provided automatically by the
267. ethod ILOWHI 0 or at a set of uniformly spaced parametric points on each patch in the higher order method ILOWHI 1 If IPNLBPT 0 the body pressure is evaluated at points on the body which are specified by the user in a special input file gdf bpi Body Point Input The format of this file is as follows header NBPT X 1 Y 1 Z 1 X 2 Y 2 Z 2 X NBPT Y NBPT Z NBPT The filename of this file must be the same as the filename of the GDF file If IPNLBPT gt 0 the data in the bpi file is read and interpreted to be in dimensional body fixed coordinates If IPNLBPT lt 0 the data in the bpi file is read and interpreted to be in dimensional global coordinates The procedure used to evaluate the body pressure at these specified points is different in the low order ILOWHI 0 and higher order ILOWHI 1 solutions These are described separately below If ILOWHI 0 the solution is based on piecewise constant values of the potential on each panel based on colocation at the panel centroids In order to evaluate the pressure at other points an interpolation procedure is adopted This interpolation is based on the absolute value of the input parameter IPNLBPT IPNLBPT 4 is recommended when the input points are in body fixed coordinates In this case the program searches and identifies the four nearest panel centroids to each specified input point and assigns weights to each of these panels based on the inverse distance to each centr
268. ex coordinates included in the GDF file TEST22 GDF The panels or patches which represent each tank must be contiguous Separate tanks can be grouped together or interspersed arbitrarily within the description of the exterior surface It is recommended to group all of the tanks together either at the beginning or at the end of the panels patches which define the exterior surface The vertical positions of tanks can be specified arbitrarily and the free surface of each tank can be defined independently of the other tanks and the exterior free surface Two alternative options can be used to specify the elevations of the tank free surfaces depending on the parameters ZTANKFS and ITRIMWL in the CFG file If ITRIMWL 0 or if ZTANKFS is not included in the CFG file then for each tank the free surface is defined to coincide with the highest point of the panel vertices or patch corners defining that tank This option is illustrated in TEST 22 where the free surface of one tank coincides with the exterior free surface i e the plane Z 0 and the free surface of the other tank is elevated by 1m above this plane If ITRIMWL 1 and the array ZTANKFS is included in the CFG file the free surface of each tank is defined to be at the elevation above Z 0 specified by the corresponding element of ZTANKFS This option can be used to vary the filling ratio of tanks without changing the GDF inputs and also to trim the waterlines of the tanks so that the f
269. f for WAMIT After the installation README file will automatically open with basic instructions on how to execute sample test runs Additionally a Program folder entitled WAMIT v7 DEMO is included as part of the installation which contains a link to the user manual 2 5 9 WAMITV7 DEMO Set a Welcome to the WAMITv7 DEMO Setup Wizard The Setup Wizard will install WAMITv7 DEMO on your computer Click Next to continue or Cancel to exit the Setup Wizard Dan can Figure 2 5 Initial startup window of WAMIT DEMO msi installer and wamit bat Users may use this link to open a DOS Command Prompt Window in the WAMIT DEMO install directory 2 3 STANDARD TEST RUNS Various standard test runs are available to illustrate different types of applications and features of the program The results of these test runs can be used to confirm that the installation and setup of the program have been performed correctly by the user The test runs also provide opportunities to use and modify existing input files for tutorial purposes The remainder of this Chapter is intended to guide new users through these procedures Descriptions of each test run are included in Appendix A If the WAMIT software is installed in accordance with the instructions above the re quired EXE and DLL and userid wam files will be installed in the directory c wamitv7 All required input files for the standard test runs will be
270. f VMAXOPT9 gt 0 data is output including the body index panel or patch index location of the point in dimensional body coordinates and magnitude of the fluid velocity The parameter VMAXOPT9 may be included in the configuration file cfg as explained in Section 3 7 The default value VMAXOPT9 1 0 is assigned if there is no input with the result that the above warning and outputs are not included This option can only be used if IOPTN 9 gt 0 in the Force Control File This option can be used to identify points where the representation of the body geometry is deficient in such a way that the evaluation of the fluid velocity is non physical In general the fluid velocity should be of order of magnitude one or smaller on the body surface and values which are much greater than this may be due to either sharp corners which are physically correct or defects in the representation of the body geometry which are not physically correct This option should be used with care to avoid excessive outputs If VMAXOPT9 0 0 every integration point will be output for all wave periods heading angles and symmetry planes of the body 5 9 THE LOG FILE wamitlog txt The file wamitlog txt is output during the run to provide an archival record The file includes the starting and ending time and date for each sub program copies of the principal input files and copies of the outputs in the files errorp log and errorf 1log Since the GDF input files are relati
271. f the GDF file empty tank list Note that WA MIT requires the normals on tank surfaces to be opposite those for body surfaces because the wetted side is the inside of the tank as opposed to the outside of the body Thus if your body surfaces have outward normals the tank surface normals should be inward The density of the fluid in each tank is specified in the CFG file RHOTANK 4 17 Control surfaces for mean drift forces A new analysis option in WA MIT version 6 3 is evaluation of mean drift forces and moments by means of momentum flux through a control surface surrounding the body The control surface is defined in a control surface file CSF extension with two format options ICDEF 0 low order similar to a low order GDF or ICDEF 1 higher order similar to a higher order GDF The control surface can be modeled in MultiSurf For ICDEF O it can consist of any type of surfaces including Trimmed Surface triangle meshes or Composite Surfaces For ICDEF 1 it can consist of any type of surface except Trimmed Surfaces and Composite Surfaces The control surface can be part of the same MultiSurf mode as the body surfaces or it can be a completely separate model file CSF export is now on the MultiSurf menu under File Export3D WAMIT 5 GDF file format A GDF file represents geometry for a single body WAMIT s GDF file has a new format option with IGDEF 2 specifying geometry to be obtained from an M S2 modal file
272. face in each tank 1 1 1 1 0 3 14 1 1 0 000000 VCG 1 000000 0000000 0000000 0000000 1 000000 0000000 0000000 0000000 1 000000 XPRDCT 0 NBETAH 2 NFIELD 1 1 0 1 0 1 0 2 1 0 1 0 0 0 Input file test22 csf test22 csf FPSO rectangular outer boundary 1 ILOWHICSF O 1 ISX ISY O 0 2 NPATCH ICDEF PSZCSF 1st two indicate this is automatic 0 2 0 RADIUS DRAFT of outer box 0 0 signifies outer bdry defined below NPART nvo THE FOLLOWING IS AN ALTERNATIVE CSF FILE WHICH IS NOT READ BY THE PROGRAM UNLESS IT IS INTERCHANGED WITH THE FILE ABOVE test22 csf FPSO circular outer boundary 1 ILOWHICSF O 1 ISX ISY 0 O 2 NPATCH ICDEF PSZCSF 1st two indicate this is automatic 12 0 2 0 RADIUS DRAFT of outer box 0 NPART In test22a the waterline is trimmed with a roll angle of 15 degrees The draft is increased by 1m in the GDF file and a vertical trim XTRIM 1 1 0 is specified in the CFG file giving a mean depth that is approximately the same as in test22 In this manner one ensures that the entire submerged portion of the hull surface is correctly defined Since the draft is increased in the GDF file it is necessary to lower the tank bottoms by the same amount thus the lower edges of the tank patches in test22a gdf are 1m lower than in test22 gdf As a result of the trim angle the center of buoyancy and center of gravity are shifted The tank volumes are unchanged from TEST22 but the displaced volume of the hull is reduced
273. face surrounding the body in the fluid In general for a floating body which intersects the free surface the control surface must start from the body s waterline either extending outward on the free surface or downward away from the waterline into the fluid Simple examples include a hemisphere or circular cylinder with sufficiently large dimensions so that the body is entirely within the interior of this surface together with the intermediate portion of the free surface between the outer control surface and the body waterline For multiple bodies the control surface for each body should not include or intersect with other bodies but it can intersect with other control surfaces In principle the position and shape of the control surface are arbitrary From a practical standpoint the control surface should be sufficiently far from the body to ensure robust evaluation of the field velocity and pressure but not so far as to require a very large number of field point evaluations Simple geometrical description of the control surface is usually desirable If the Alternative 1 method is used there is no contribution to the horizontal drift force and vertical drift moment from any part of the control surface that is in the plane of the free surface z 0 Thus if these are the only required components of the drift forces the control surface can be completely separated from the body surface without the need to include the intermediate portion of
274. file after these four lines depending on the manner in which the geometry of the body is represented See Sections 7 5 7 8 The data on the first three lines are identical to the low order method as described in Section 6 1 Thus header denotes a one line ASCII header dimensioned CHARACTER 72 ULEN is the dimensional length characterizing the body dimensions used to nondimen sionalize the quantities output from WAMIT GRAV is the acceleration of gravity using the same units of length as in ULEN ISX ISY are the geometry symmetry indices which have integer values 0 1 to denote no symmetry or symmetry about the plane x 0 or y 0 respectively The data on line 4 of the GDF file are defined as follows NPATCH is equal to the number of patches used to describe the body surface as explained in Section 7 1 If one or two planes of symmetry are specified NPATCH is the number of patches required to discretize a half or one quadrant of the whole of the body surface respectively IGDEF is an integer parameter which is used to specify the manner in which the geometry of the body is defined Four specific cases are relevant corresponding respectively to the representations explained in Sections 7 5 7 6 7 7 and 7 8 IGDEF 0 The geometry of each patch is a flat quadrilateral with vertices listed in the GDF file IGDEF 1 The geometry of each patch is represented by B splines with the correspond ing data in the GDF fil
275. file conversion utility Inthe WAMIT RGKernel interface we have made the global reversal of normals optional The choice is signaled on a per body basis by the inward normal flag in the GDF file see bd ow This results in two options for the MultiSurf user who is building a mode for the WAMIT RGKernel interface 1 Build the model with all unit normals pointing inward WAMIT s convention and set the inward normal flag to 1 or 2 Build the model with all unit normals pointing outward and set the inward normal flag to O We prefer option 2 because the outward normals are easier to see In either case the orientation flags of the individual surfaces can be freely used in achieving the desired consistent orientations 4 5 Base plane and waterline In MultiSurf there are no restrictions on the location and orientation of geometry but there are some sensible choices that will make the process easier Vertical position M ost models for WA MIT analysis are built in one of three vertical positions Either 1 The model is built above a base plane so the lowest Z coordinates are zero and the design waterline is at some positive Z call it Zwl gt 0 or 2 The model is built with Z 0 as the design waterline so the lowest parts of the wetted surface are at a negative Z call it Zdraft lt 0 or 3 The model is built with the point representing its center of gravity C G at the origin Any of these approaches works fine
276. fluid velocities on the body panels NOOUT 111101111 This option can be useful to avoid very long OUT files since the data for option 5 is generally much more extensive than for the other options The default value NOOUT D 1 for J 1 9 is assigned if NOOUT is not included in the configuration file The data for each specified option is always included in the corresponding numeric output file regardless of the array NOOUT NPDIPOLE is an integer array used to specify the panel or patch indices of zero thickness elements represented by dipoles Multiple lines of input can be used but each line must begin with NPDIPOLE The data on these lines may specify either individual indices of each dipole panel patch or ranges of consecutive indices which are indicated by enclosing a pair of indices in parenthesis The following three examples are equivalent ways of specifying that the indices 2 4 5 6 8 are dipole panels or patches NPDIPOLE 2 45 6 8 NPDIPOLE 2 4 6 8 NPDIPOLE 2 2 4 6 8 8 Note that parenthesis must be used to denote the lower and upper limits of a range of consecutive indices and parentheses must not be used for any other purpose Other ASCII characters may be included on these lines and are ignored It is not necessary for the individual indices or ranges to be in ascending order except for the first and last indices of each range enclosed in parentheses The Version 6 option to define dipole panels or
277. for inputting these parameters gdf spl config wam NONE NU NV PANEL SIZE error KU KV KSPLIN 3 IQUO IQVO IQUADO 3 IQULIQVI IQUADI 4 Here the first column indicates inputs in the optional SPL file and the second column indicates the corresponding inputs in the CONFIG WAM file The third column indicates the default values which are set if there is no SPL file and if the parameters are not included in the configuration files It is important not to specify the same parameters in both the SPL and configuration files since this will cause errors reading the data in the SPL file In summary the simplest way to use the higher order method is to specify PANEL_SIZE only in the CONFIG WAM file and ignore all of the other parameters shown in this table The values of these parameters are displayed for each patch in the header of the out file When the parameter PANEL_SIZE is used its value is also displayed on the line indicating that the higher order method is used 7 13 ADVANTAGES AND DISADVANTAGES OF THE HIGHER ORDER METHOD Some advantages and disadvantages of the higher order method in comparison of the low order method are listed below Advantages 1 The higher order method is more efficient and accurate in most cases More precisely the higher order method converges faster than the low order method when the number of panels is increased in both Comparisons for various geometries can be found in 18 19 Thus accurate solutions
278. for the vertical components of the drift force and horizontal components of the drift moment since these require evaluations of the fluid velocity close to and on the body waterline Thus the option to use ISOR 0 with ILOWHI 0 to evaluate the Option 7 drift forces should be restricted to applications where only the horizontal drift force and vertical moment are required 11 1 CONTROL SURFACE FILE CSF The geometry of the control surface can be described in the same manner as the body geometry Similar options exist to define the control surface and different options can be used for the control surface and for the body In the low order method specified by inputting the parameter ILOWHICSF 0 on line 2 of the CSF file the control surface is represented by quadrilateral panels in the same manner as described for the body in Chapter 6 In the higher order method ILOWHICSF 1 is assigned on line 2 of the CSF file and the control surface is represented in the same manner as described for the body in Chapter 7 using any of the options available for higher order representation of the body surface including flat panels B splines MS2 files and using subroutines in GEOMXACT The format of the CSF file is almost identical with the GDF file The principal difference is on line 2 where the parameters ULEN and GRAV in the GDF file are replaced by ILOWHICSF Also when ILOWHICSF 1 the parameter PSZCSF is specified in the CSF file to control the accuracy of the
279. free surface inside the tank If ZTANKFS is included in the CFG file and if ITRIMWL 1 the geometry of internal 12 8 tanks is trimmed using the same algorithms as for the exterior surface In this case it is necessary to define the tank geometry up to the level of the trimmed free surface as in TEST22A Special attention is required also when irregular frequency removal is used IRR gt 0 If the interior free surface is defined by the user as part of the overall geometry of the body IRR 1 it is necessary to ensure that the interior free surface coincides with the Z 0 plane after trimming If automatic discretization of the interior free surface is used IRR 3 the interior free surface is defined correctly in the plane of the trimmed free surface The option IRR 2 cannot be used when ITRIMWL gt 0 See Section 10 2 12 3 RADIATED WAVES FROM WAVEMAKERS IN TANK WALLS Different options are available for the analysis of problems where walls are present in the plane s of symmetry x 0 and or y 0 The analysis of wave radiation by wavemakers in the plane s of the walls is discussed in this Section A more general approach applicable to wavemakers in the planes of the walls and or bodies in the interior domain of the fluid is described in Section 12 4 These two approaches require somewhat different inputs Either one tank wall of infinite width or two semi infinite walls at right angles can be considered These correspond to one or bo
280. frequencies Chapter 10 Chapter 11 describes the procedure for evaluating the mean drift forces and moments by integration of the momentum flux on a control surface which surrounds the body in the fluid Chapter 12 describes additional extensions to include the dynamics of fluid in internal tanks trimmed waterlines radiated waves from wavemakers interactions of bodies and wavemakers with vertical walls applications where part or all of the body surface consists of free surfaces with oscillatory pressures and a simplified method to include or omit parts of the body surface when integrating the pressure force and moment Chapter 13 describes the utility F2T Frequency to Time domain which is used to transform the linear WAMIT outputs to the corresponding time domain impulse response functions Chapter 14 describes various computational topics including temporary data storage numbers of unknowns and input parameters to provide a qualitative basis for estimating the requirements for RAM and hard disk storage and for estimating run times Instructions 1 2 are provided for using multiple processors and extended RAM to reduce run times Section 14 7 outlines the procedure for modification and use of dll files to describe the geometry and generalized modes Section 14 8 lists the reserved filenames used by the program Section 14 9 describes an alternative procedure to evaluate field pressures and velocities when the number of field points is v
281. ges which are generated during the run The intermediate data transfer file which is described briefly in Section 5 10 is a binary file used internally in WAMIT to transfer data from the POTEN to FORCE 5 1 THE FORMATTED OUTPUT FILE OUT The formatted output file frc out is written in the sub program FORCE to summarize inputs and outputs The principal inputs are in the header portion of the file including licensing information input filenames run times and dates and hydrostatic data The hydrodynamic outputs are written in sequence for each wave period heading angle and parameter Appropriate text labels are included to identify the data 5 1 If an old file exists with the same name in the same directory the user is interrogated with options to over write the old OUT file or to assign a different name to the new file This interruption can be avoided by renaming or deleting the old file Often when different options or variants of the inputs are being compared it is convenient to assign a new name which is related to the old name in a logical manner This situation can be avoided by using different filenames for the corresponding FRC input files even if the files are the same 5 2 NUMERIC OUTPUT FILES Separate output files of numeric data are generated for each of the nine options of the FORCE subprogram listed in Section 4 3 The hydrodynamic parameters in these files are output in the same order as in the OUT file and listed i
282. gt Break before CALL SOLVE period JPER The value displayed for JPER is the index of the current wave period If the run is terminated with JPER 1 there will be no outputs except for the header information and hydrostatics To minimize the amount of wasted computations it is most efficient to break the run at the start of the period loop with JPER gt 1 instead of after the setup of the linear system is completed Following the above message the menu prompts the user to select one of three options with the following display on the monitor File BREAK WAM exists Select option b c d b Break run and continue with reduced NPER c Continue run and keep BREAK WAM 4 44 d Delete BREAK WAM and continue run Enter b c or d The results of these three options are as follows b The execution of POTEN is terminated and NPER JPER 1 is assigned for the remain der of the run c The execution of POTEN is continued to the next break point d The file BREAK WAM is deleted and execution of POTEN is continued without further breaks The inputs b c d are not case sensitive either lower case or upper case letters may be used Inputting any other characters will result in a repeat of the above menu of options until either b c or d is input Since the file break wam is not read the data in this file is arbitrary One conve nient possibility when break points are requested is to copy a small existing file such as fnames wam to br
283. h body 8 2 8 1 If IALTFRC 1 the format of the FRC file is as shown below header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 VCG 1 XPRDCT 1 1 1 XPRDCT 2 1 1 XPRDCT 3 1 1 VCG 2 XPRDCT 1 1 2 XPRDCT 2 1 2 XPRDCT 3 1 2 XPRDCT 1 2 1 XPRDCT 2 2 1 XPRDCT 3 2 1 XPRDCT 1 2 2 XPRDCT 2 2 2 XPRDCT 3 2 2 INPUT TO FORCE IALTFRC 1 XPRDCT 1 3 1 XPRDCT 2 3 1 XPRDCT 3 3 1 XPRDCT 1 3 2 XPRDCT 2 3 2 XPRDCT 3 3 2 VCG N XPRDCT 1 1 N XPRDCT 1 2 N XPRDCT 1 3 N XPRDCT 2 1 N XPRDCT 2 2 N XPRDCT 2 3 N XPRDCT 3 1 N XPRDCT 3 2 N XPRDCT 3 3 N NBETAH BETAH 1 BETAH 2 NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 BETAH NBETAH XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD The only difference relative to the case of a single body Section 4 3 is that the VCG and 3 x 3 matrix of each body s radii of gyration are entered in succession 8 3 8 2 INPUT TO FORCE IALTFRC 2 If IALTFRC 2 the format of the FRC file is the same as described in Section 4 4 for a single body except that the array specifying XCG YCG ZCG is extended to include all bodies and the external force matrices have dimensions NDFR x NDFR NDFR ZAL 6 NEWMDS n is the total number of degrees of freedom including all rigid body modes and generalized modes The normal format is as follows header IOPT
284. h is in the plane of the free surface and only in contact with the fluid on the lower side should be considered as part of the conventional surface S 15 8 MEAN DRIFT FORCES BASED ON PRESSURE INTE GRATION Figure 15 1 Coordinate systems fixed with respect to the body dashed lines and its mean position solid lines The instantaneous position vector X in an inertial coordinate system of the point fixed on the body fixed coordinate system 7 is given by X ax HE 15 48 For the present purpose we consider only the first order quantities of the translational modes the rotational modes and the velocity potential q The roll pitch yaw sequence of rotations is adopted and the transformation matrix is given by 1 ag a3 0 0 H z 201A ay a3 0 15 49 20103 20203 ay 2 The normal vector in the inertial coordinate system can be expressed by gt N n axa Hn 15 50 where 7 is the normal vector on the body boundary in the body fixed coordinate system 15 11 The pressure at the instantaneous position x given in the equation 15 48 can be expressed by P pfg z Zo de g 3 ary A22 5Ve Vo E ax T Voi gH Vz 15 51 where Z is the vertical coordinate of O relative to the free surface The mean forces and moments are obtained by time averaging the following expressions for the forces and moments FO _ NPds 15 52 Sb 2 X x
285. h their filenames listed in the POT file as shown in Sections 4 2 The individual GDF files for each body are unchanged from the case where N 1 thus GDF files can be combined without modification to analyze multiple body configurations However the units of measurement identified by the parameter GRAV must be the same for all bodies The program assigns GRAV based on the value in the GDF file for the first body K 1 If the value of GRAV for another body differs from this by more than a small tolerance GTOL 0 1 the run is terminated with an appropriate error message Except for the special cases described in Section 8 5 WAMIT assumes that there are no planes of hydrodynamic symmetry when N gt 1 If geometric symmetry is specified for individual bodies via their respective GDF input files the program reflects about the corresponding planes and increases the number of panels accordingly The total number of unknowns is the sum of the number required to describe each body including reflections 8 1 Thus the run times and memory requirements are substantially increased When N gt 1 walls can be defined using the procedure described in Section 12 4 The multiple body extensions are essentially the same for analyses based on the low order and higher order methods However it is impossible to use both methods simultane ously for different bodies The GEOMXACT subroutines described in Section 7 8 can be used for multiple bodies but spe
286. he accuracy and efficiency of the solution and exploit the capabilities of a wide range of contemporary computing systems ranging from personal computers to supercomputers Important features include the use of special algorithms for the evaluation of the free surface wave source potential the option to use direct iterative or block iterative solution algorithms for the complex matrix equation and the option to use either the low order or higher order panel methods Version 7 has been developed to exploit the additional features of multiple processors 64 bit operating systems and optimum use of available RAM In combination these result in a fast versatile and robust code capable of analyzing a wide variety of offshore structures 1 4 WAMIT consists of two subprograms POTEN and FORCE which normally are run sequentially POTEN solves for the radiation and diffraction velocity potentials and source strengths on the body surface for the specified modes frequencies and wave headings FORCE computes global quantities including the hydrodynamic coefficients motions and first and second order forces Velocities and pressures on the body surface are evaluated by FORCE Additional field data may also be evaluated by FORCE including velocities and pressures at specified positions in the fluid domain and wave elevations on the free surface Since the principal computational burden is in POTEN the intermediate output data from this subprogram is
287. he NEWMODES DLL file is used to define the generalized modes Input file test08 cfg TESTO8 CFG bending of vertical column with 4 generalized modes ilowgdf 1 ipltdat 5 NUMHDR 1 NUMNAM 0 ISOR 0 IRR 0 MONITR 0 NEWMDS 4 IALTFRC 2 Input file test08 pot TESTO8 POT bending of vertical column at resonance 200m depth 200 0 HBOT o 0 IRAD IDIFF 1 6 5 1 0 0 1 NBODY test08 gdf 0 0 0 0 0 0 0 0 o 0 0 O0 O 90 First 10 lines of input file test08 gdf TESTO8 GDF vertical cylinder 16 32 cosine spacing at free surface 1 0000 9 80665 1 1 512 10 0000 0 000000 200 000 9 95185 0 980171 200 000 9 95185 0 980171 190 186 10 0000 0 000000 190 186 10 0000 0 000000 190 186 9 95185 0 980171 190 186 Input file test08 frc TESTO8 FRC file vertical column with 4 bending modes 1 1 1 1 0 0 0 o 0 1 0 0000000 0000000 1 000000 1 0 0 0 O O 0 O O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 0 O O 0 O O O 0 O 0 O O O 0 69115 62832 62832 62832 O 0 O O 0 O 62832 67320 62832 62832 0 0 0 O O 0 62832 62832 663283 62832 O 0 O O O 0 62832 62832 62832 65688 0 1 O 0 O O 0 O 0 O 0 0 O 0 O O 0 O 0 O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 O O 0 O 0 O 0 0 O 0 O O O 0 O O O O 0 0 O O 0 O 103044 412177 824354 1339575 0 0 O O O 0 41
288. he file test22 csf for illustration but it is not read by the program unless it is moved to the top of the file In the second case the outer boundary is circular and PSZCSF is positive indicating that automatic subdivision of the control surface is performed as described in Section 11 4 The corresponding output for the mean drift force and moment is contained in the file TEST13 7 Comparison of the results for the mean drift force in the sway direction from the files TEST22 9 direct pressure integration and TEST22 7 control surface with the far field momentum drift force data in TEST22 8 confirms that the control surface gives a more accurate result compared to direct pressure integration for this body Input file test22 cfg TEST22 CFG fpso with 2 interior tanks ipltdat 4 ILOWHI 1 ILOG 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 MONITR 0 NUMHDR 1 NOOUT 111101111 NPTANK 8 11 12 15 RHOTANK 1 0 1 0 relative densities of tank fluids ITANKFPT 1 tank field points are in frc file Input file test22 pot TEST22 POT fpso with 2 interior tanks 1 0 1 1 IRAD IDIFF 3 2 0 2 5 3 0 1 NBETA array BETA follows 90 1 NBODY test22 gdf 0 0 0 0 XBODY 1 1 1 1 1 1 IMODE 1 6 Input file test22 gdf TEST22 GDF fpso with 2 tanks one raised joined at x 0 1 9 80665 ULEN GRAV O 1 ISX ISY 15 21 NPATCH IGDEF 36 NLINES 4 16 2 3 15 2 XBOW XMID XAFT 2 2 1 2 HBEAM HTRANSOM 1 2 0 6 DRAFT DTRANSOM
289. he four corners of each patch If the patch intersects the waterline an iterative procedure is used to remap the submerged por tion onto a square domain in parametric space There are situations where this procedure breaks down and thus it must be used with caution One example is where the vertices of a patch are all submerged but a portion of one side maps in physical space above the free surface Body symmetry can be affected by trimming When it is necessary WAMIT auto matically reflects the body geometry and resets the symmetry indices For example in TESTOIA the GDF file specifies ISX ISY 1 but the trimmed body has only one plane of symmetry x 0 Similarly in TEST22A the GDF file specifies ISY 1 but the trimmed body has no planes of symmetry due to the heel angle Dipole panels are trimmed in the same manner as conventional panels as illustrated in TESTO9A Special attention is required for bodies with internal tanks Two alternative options are included as explained in Section 12 1 depending on the parameter array ZTANKFS in the CFG file If ZTANKFS is not included in the CFG file or if ITRIMWL 0 the geometry of internal tanks is not trimmed and the tank free surface is always defined by the highest points of the specified panels or patches If trimming includes a pitch or roll displacement of the body this approach requires the tank geometry to be redefined so that its upper boundary coincides with the correct plane of the
290. he inner Gauss quadrature parameter IQUI for all patches when the higher order method is used ILOWHI 1 The default value is IQUADI 4 See Sections 7 11 12 IQUADO is an integer parameter specifying the order of the outer Gauss quadrature parameter IQUO for all patches when the higher order method is used ILOWHI 1 The default value is IQUADO 3 See Sections 7 11 12 for further information IREADRAO is an integer parameter specifying if the RAO s are to be input from an external file as explained in Section 4 3 IREADRAO 0 Use RAO s computed by WAMIT in Option 4 to evaluate Options 5 9 IREADRAO 1 Evaluate only Options 1 2 3 4 IREADRAO 2 Read RAO s in complex format from an external file to evaluate Options 5 9 IREADRAO 3 Read RAO s from modulus and phase in an external file to evaluate Options 5 9 The default value is IREADRAO 0 IRR is the integer used to specify whether the irregular frequencies are removed The use of IRR is described in Chapter 9 IRR 0 Do not remove the effect of the irregular frequencies IRR 1 Remove the effect of the irregular frequencies User needs to represent the interior free surface by panels or patches IRR 2 Remove the effect of the irregular frequencies Program projects the body panels on the interior free surface This option is restricted to the low order method ILOWHI 0 IRR 3 Remove the effect of the irregular frequencies Program automatically discretize
291. he velocity potentials pj 7 1 7 15 2 INTEGRAL EQUATIONS FOR THE VELOCITY POTEN TIAL In WAMIT the boundary value problems defined above are solved by using Green s theorem to derive integral equations for the radiation and diffraction velocity potentials on the body boundary The integral equation satisfied by the radiation velocity potentials p on the body boundary takes the form omy x x ff A E d JA n G E x 15 11 Here Sp denotes the wetted surface of the body in its fixed mean position below the plane z 0 The corresponding equation for the total diffraction velocity potential yp is OG E x angola ff pole EER ag srpa 15 12 Sp One The diffraction potential may also be obtained from equation 15 8 after solving for the scattered potential ys The equation for the scattered velocity potential is Imps x jelk gpa N Jf lag x d 15 13 One From the computational point of view equation 15 12 has some advantages over 15 13 in terms of cpu time and the requirement of storage space because of the relative simplicity of the right hand side The Green function G x is referred to as the wave source potential It is the velocity potential at the point x due to a point source of strength 47 located at the point It satisfies the free surface and radiation conditions and in infinite water depth is defined by 1 1 2K pe eeto m e yam 2 0 151 r x E y n
292. he velocity potential is expressed by a distribution of sources only in the form ff eat gde 15 24 After discretizing the body surface with plane panels with constant source strength on each panel the potential is expressed by Sat J Cea 15 25 Denote the normal vector as 7 and the two tangential unit vectors as 5 and t on each panel The three components of the velocity are then given in the 7 5 t coordinate system as follows nl 2mo xs DD o x ff Gui EdE 15 26 plx Dol ff Golos EdE 15 27 eli DD x ff Gxt 15 28 15 5 DISCRETIZATION OF THE INTEGRAL EQUATIONS IN THE HIGHER ORDER METHOD ILOWHI 1 The mean body surface is defined by patches as explained in Chapter 7 Each patch must be a smooth continuous surface The Cartesian coordinates x x y z of a point on the patch are expressed in term of two parametric coordinates u u v These are normalized so that they vary between 1 in the domain of the patch Details of the geometric description of the body surface are provided in Chapter 7 The velocity potential on each patch is represented by a product of B spline basis functions U u and V v as shown in equation 7 4 The total number of B spline basis functions on each patch is M times M Upon substituting equations 7 3 and 7 4 15 11 can be expressed in the form My Mu My Mu joo us 2 eU d JU u J Ra z Enio ue S Sf fuja up J u 15 29 where U
293. hinge modes 1 0 0 2 3 5 1 180 1 test24 gdf 0 0 0 Os 0 1 0 1 1 0 IRAD IDIFF NPER array PER follows NBETA array BETA follows NBODY XBODY IMODE 1 6 Input file test24 gdf TEST24 segmented vessel with 7 segments 1 9 80665 ULEN GRAV 1 1 ISX ISY 4 32 NPATCH IGDEF 3 NLINES 7 Nsegments 1 Radius 2 6 8 10 xseg Input file test24 spl TEST24 segmented vessel with 7 segments 42 NU NV mid cylinder 44 next cylinder 42 outer cylinder 44 spheroidal end Input file test24 frc TEST24 segmented vessel with 7 segments and 4 hinge modes 1 1 1 1 O0 O O O 1000 0 0 0 1 29321 5 O O O 0 O 0 O 0 O 0 29321 5 O O 0 O 0 O 0 O 0 O 29321 5 0 O O 12000 O 12000 O 0 O O 1 5E4 0 O 0 O 0 O 0 O O 0 7 33E5 0 O 24000 O 72000 O O O 0 O 7 33E5 0 O 0 O 0 O 12000 O 0 O 10000 O 2000 O 0 O O O 24000 0 O 6000 O 2000 0 O 12000 O 0 O 2000 O 8000 O 0 O 0 O 72000 O O 2000 O 8000 O 000 A 25 AIR CUSHION VESSEL WITH PRESSURE CHAMBERS TEST25 The vessel consists of two air chambers surrounded by rectangular skirts The length is 20m beam 10m and draft 2m The width of the skirts is Im The free surface in the chambers shown by red shading in the figures below is 1m below the exterior free surface One quadrant of these surfaces is represented by flat quadrilateral patches in the GDF file with two planes of symmetry Two pr
294. hus it is possible for the user to include comments at the ends of selected lines in the input files to identify the data on these lines Such comments should be separated from the data by at least one blank space This format is illustrated in the input files in Appendix A Generally comments at the ends of appropriate lines which contain non numeric ASCII characters will ensure that execution is interrupted with an error message if insufficient data is contained on the line When blocks of data are written on multiple lines and read by a single READ statement comments are only permitted after all of the data is read In the POT file for example comments can be placed after the last elements of the arrays PER and BETA but not on intermediate lines which contain these arrays and similarly for field point coordinates in the FRC file All lines of data in input files which contain ASCII text must be restricted to columns 1 80 4 11 UNIFORM ARRAYS OF FIELD POINTS In some applications large numbers of field points are required with a spacing on a rect angular grid This can be facilitated by assigning the parameter IFIELD ARRAYS 1 in the CFG file as explained in Section 4 7 When IFIELD_ARRAYS 1 additional data is appended to the FRC file immediately after the line s containing NFIELD and XFIELD The following shows the complete Alternative 1 FRC file replacing the format shown in Section 4 3 header IOPTN 1 IOPTN 2 IOPTN 3 IOP
295. icons in the tree below to change the way features will be installed SS WAMIT Program Supplemental DLLs geomxact and 2 Main Program newmodes and associated sources H Supplemental Dlls Do NOT install if using your own MultiSurf Components custom DLLs 3 Sample Test Runs amp Source and Utilities This feature requires 440KB on your Documentation hard drive Program Menu Browse Reset Disk Usage Bak Net Cance Figure 2 4 Custom installation directory configuration window for site licenses The PC executable Version 7PC includes additional dynamic link library files DLL which must be installed in the same directory i e folder as the executable file wamit exe or in a different folder which is included in the system path By default the msi installer does this for the user If these DLL files are missing the program will not run regardless of the inputs and options specified The required DLL files include special WAMIT DLL files and also special Intel or Microsoft DLL files The three required WAMIT DLL files are geomxact dll newmodes dll rg2wamit dll The extended Version including the capability to input MultiSurf models requires one additional DLL file rgkernel d11 and an extended version of rg2wamit d11 as explained in Section 7 7 Version 7PC is compiled using Intel Visual Fortran IVF Version 12 1 The following DLL files are require
296. ignify if the external damping matrix EXDAMP is read If the value of the index is zero the matrix EXDAMP is not included in the FRC file and the program assumes that all values in this matrix are zero If the value of the index is one the matrix EXDAMP is included in the FRC file EXDAMP is the 6 NEWMDS x 6 NEWMDS dimensional damping matrix of an arbitrary external force or moment acting on the body e g from a mooring cable subject to viscous damping The value of each element in this matrix is added to the corresponding linear wave damping coefficient of the body in setting up the equations of body motions ISTIF This index is either 0 or 1 to signify if the external mass matrix EXSTIF is read If the value of the index is zero the matrix EXSTIF is not included in the FRC file and the program assumes that all values in this matrix are zero If the value of the index is one the matrix EXSTIF is included in the FRC file EXSTIF is the 6 NEWMDS x 6 NEWMDS dimensional stiffness matrix of an arbi trary external force or moment acting on the body e g from an elastic mooring cable In setting up the equations of body motions the value of each element in this matrix is added to the corresponding restoring coefficient of the body including both hydrostatic pressure and the gravitational moment due to the body s mass as defined in Section 3 1 The vertical inertia force due to heave EXMASS 3 3 is assumed equal to the body mass and i
297. ile FRC with the extension frc All WAMIT input files are ASCII files The first line of most files is reserved for a user specified header consisting of up to 72 characters which may be used to identify the file If no header is specified a blank line must be inserted to avoid a run time error reading the file The remaining data in each file is read by a sequence of free format READ statements Thus the precise format of the input files is not important provided at least one blank space is used to separate data on the same line of the file Further details regarding the formats and names of files are contained in Section 4 10 Following the implicit FORTRAN convention parameter names beginning with I J K L M or N denote integers and all other numeric parameters are represented by real decimal format numbers It is good practice to represent real numbers including a decimal point and not to use a decimal point for integer parameters Additional input files may be used to select various options and to optimize the com putations for specific applications The file fnames wam is used to specify the names of the CFG POT and FRC input files to avoid interactive input of these names see Section 4 8 The configuration files config wam and pot cfg are used to configure WAMIT and to specify various options as described in Section 4 7 The optional input file break wam may be used to set break points in the execution of POTEN as described in
298. ile gdf MOD for MODes contains the generalized normal velocity on each panel and the hydrostatic coefficients These two files are prepared automatically by WAMIT and DEFMOD and do not require special attention by the user The first run of WAMIT is made with NEWMDS gt 0 specified in the configuration file The pre processor file gdf PRE is output to the hard disk and execution of WAMIT is interrupted with the following message PREMOD run completed now run DEFMOD This first run of WAMIT is interrupted if NEWMDS gt 0 and if there is not already in the default directory an input file with the name gdf MOD For this reason the user must rename or delete old MOD files prepared with the same gdf filename The output file gdf PRE includes a one line header for identification followed by one line containing the symmetry indices ISX ISY number of input panels NEQN and the maximum number of degrees of freedom which can be assigned in the WAMIT run MAXDFR Each of the remaining lines of this file corresponds to a panel in the same order as the GDF file and includes the coordinates x z y z of the panel centroid its area and the six components of the normal vector n and cross product x xn Either before or after the first run of WAMIT the user should modify the subroutine DEFINE in the program DEFMOD specifying the number of generalized modes their symmetries with respect to the geometric planes of symmetry of the body
299. implemented is that the definition of the body geometry in the GDF file must include all surface elements which are submerged when the body is trimmed Thus it is necessary to define a sufficient portion of the body surface above the untrimmed waterplane Trimming of the waterline is supported in both the low order ILOWHI 0 and higher order ILOWHI 1 methods There are some practical restrictions that must be considered when the higher order option is used as described below The trimmed condition of the body is specified by two parameters in the configuration files ITRIMWL and XTRIM as defined in Section 4 7 ITRIMWL 0 is the default indicating that the body is not trimmed ITRIMWL 1 specifies that the body is trimmed and XTRIM 1 3 specifies the vertical elevation and angles of rotation of the body as explained below If ITRIMWL 0 XTRIM is ignored Note that if ITRIMWL 0 or ITRIMWL is not included in the inputs then the GDF file must only define the submerged portion of the body as in previous versions of WAMIT in this case the program checks to ensure that no elements of the body surface are above the plane of the free surface and an error stop occurs if such elements are detected Conversely when ITRIMWL 1 elements of the body surface above Z 0 are permitted and there is no check or error stop It is possible to suppress the error stop without trimming with the inputs ITRIMWL 1 and XTRIM 0 0 0 0 0 0 Appendix A includes four
300. in RGKLOG TXT In the truncated cylinder example modeling the side and bottom surfaces as two separate surfaces rather than one surface with a breakline would have the advantage of making it easier to utilize cosine spacing to better resolve the rapidly changing potential around the chine 4 13 Cosine spacing The phrase cosine spacing refers to systematic refinement of the mesh in regions where gradients are high to provide better resolution in these areas Although we don t have a mesh anymore in the usual sense of a panel file the concept of cosine spacing is in fact still quite pertinent and the techniques for achieving it are highly similar to those used for the low order method Exterior corners chines are the typical places where cosine spacing improves solution accuracy Also accuracy benefits are experienced with cosine spacing near the free surface In MultiSurf there are two common techniques for achieving mesh concentration 1 Relabeling of lines curves snakes and surfaces 2 Type 2 B spline lofted surfaces BLoftSurfs with duplicate master curves at the ends also usually for flat rectangular patches B spline surfaces BSurfs with duplicate control points at corners and or edges 4 14 Parameters As described below the GDF file can contain any number of parameter lines which override specified floating point data values in the model The format of a parameter line is just ent
301. in Tests 06 07 and 14 where a TLP with two planes of symmetry is analyzed only in head seas BETA 0 with IDIFF 0 and IMODE 0 for sway roll and yaw in this case the complete diffraction solution is symmetric about the plane Y 0 and the above inputs give correct results for Options 5 9 VCG Dimensional z coordinate of the center of gravity of the body relative to the origin of the body system input in the same units as the length ULEN XPRDCT is the 3x3 matrix of the body radii of gyration about the body fixed axes where 1 J 1 2 3 correspond to x y z respectively input in the same units as the length ULEN More precisely the elements of the body inertia matrix m are evaluated for i j 4 5 6 according to the algorithm m m x XPRDCT i 3 j 3 x XPRDCT i 3 7 3 Here the body mass m is evaluated from the displaced mass of fluid and the absolute value is used in the last factor so that negative products of inertia can be specified The remaining elements of mi are evaluated assuming the body is freely floating in equilibrium based on the calculated values of the displaced volume and center of buoyancy and on the specified value of VCG In practical cases the matrix XPRDCT is symmetric Zeroes may be specified if the body motions are not evaluated NBETAH is the number of Haskind wave headings defined below NBETAH must be an integer greater than or equal to zero BETAH is an array of length NBETAH defined as the
302. in elements represented by dipole patches on the plane of symmetry As an example when a keel on the centerplane y 0 is represented by dipole patches either the port or starboard side of the vessel can be defined in the GDF file with ISY 1 The following discussion applies in all cases except IGDEF 2 i e exclusive of the option to use MultiSurf geometry as described in Section 7 7 The recommended procedure to define dipole patches with MultiSurf is explained in Appendix C In that case the dipole patches are identified in the gdf ms2 file output from MultiSurf and input to WAMIT No reference to the dipole patches should be included in the CFG file To analyze bodies with zero thickness elements for IGDEFZ 2 the corresponding dipole patches are identified in the configuration files using the parameter NPDIPOLE The indices of the dipole patches are defined by including one or more lines starting with NPDIPOLE followed by the indices or ranges of indices of the dipole patches as ex plained in Section 4 7 In earlier versions of WAMIT it was possible to define dipole patches in an alternative manner by specifying extra data in the GDF file That alternative is not supported in Version 7 as explained in Section 4 1 The utility v6v7inp described in Appendix B converts old GDF files using that alternative to the format required in Version 7 and adds the appropriate data for NPDIPOLE in the CFG file 7 11 THE OPTIONAL SPLINE CONTROL
303. inates X Y Z and their total number NPAN are restricted to one quadrant or one half of the body namely the portion x gt 0 and or y gt 0 Conversely if ISX 0 and ISY 0 the complete submerged surface of the body must be represented by panels ISX 1 The x 0 plane is a geometric plane of symmetry ISX 0 The x 0 plane is not a geometric plane of symmetry ISY 1 The y 0 plane is a geometric plane of symmetry ISY 0 The y 0 plane is not a geometric plane of symmetry For all values of ISX and ISY the x y axes are understood to belong to the body system The panel data are always referenced with respect to this system even if walls or other bodies are present NPAN is equal to the number of panels with coordinates defined in this file i e the number required to discretize a quarter half or the whole of the body surface if there exist two one or no planes of symmetry respectively X1 1 Y1 1 Z1 1 are the x y z coordinates of vertex 1 of the first panel X2 1 Y2 1 Z2 1 the x y z coordinates of the vertex 2 of the first panel and so on These are expressed in the same units as the length ULEN The vertices must be numbered in the counter clockwise direction when the panel is viewed from the fluid domain as shown 6 4 in Figure 6 1 The precise format of each coordinate is unimportant as long as there is at least one blank space between coordinates and the coordinates of the four vertices representi
304. ine discretization IALTFRC 2 1 1 1 2 0 0 0 1 1 IOPTN IOPTN 4 lt 0 signifies fixed modes 6 NDFR 110001 IMODE 1 RHO 0 0 3 0 XCG 1 IMASS 53066 4 0 0 0 159199 2 O 0 53066 4 O 159199 2 0 O 0 O 53066 4 0 0 O O 159199 2 O 8 0201552E7 0 O 159199 2 O 0 0 8 0201552E7 O 0 0 0 0 O 9 54906731E7 0 IDAMP 0 ISTIFF 0 NBETAH 0 NFIELD A 7 THE ISSC TENSION LEG PLATFORM TEST07 This test run is intended to refine the analysis of the ISSC TLP described in TESTO6 1012 panels are used on each quadrant resulting in 4048 panels for the complete structure The block iterative solver is used ISOLVE 4 to provide a relatively fast but robust solution For the sake of variety in the analysis of the diffraction problem the solution for the scattered potential is computed ISCATT 1 Alternative form 2 of FRC is used but the mass is assumed to be equal to the displacement computed by WAMIT Note that the displacement is about 4 greater than for Test Run 2 due to the more accurate description of the columns The panel vertices are defined to lie on the exact circular cylinder surface hence the flat panels define a surface with less displaced volume than the exact body Comparisons should be made with the output files from TEST06 to judge the conver gence of the results with increasing numbers of panels As explained in Appendix A 6 a warning message is displayed for Options 8 and 9 since IDIFF 0 Input file te
305. ing alternatives can be used NPER 0 Read inputs and evaluate hydrostatic coefficients only NPER gt 0 Execute the hydrodynamic analysis for NPER wave periods NPER lt 0 Execute the hydrodynamic analysis for PER wave periods as explained below If NPER 0 POTEN and FORCE will run but not execute any hydrodynamic analysis This option can be used to test for errors in input files and to evaluate the hydrostatic coefficients in the OUT file If NPER 0 the array PER must be removed from the Potential Control File Beginning in Version 7 1 multiple groups of wave periods can be defined with one or both of the above formats using the optional parameter NPERGROUP To use this option line 4 of the POT file should contain the following text NPERGROUP m where m is an integer followed by m groups of inputs specifying NPER and PER in either of the formats above This option is illustrated in the file test17a pot in Appendix A17 PER is the array of wave periods T in seconds or of optional inputs as specified by the parameter IPERIN Normally the values of PER must be positive By using the optional parameter IPERIN in the configuration file it is possible to replace the input array of wave periods by a corresponding array with values of the radian frequencies w 27 T infinite depth wavenumbers K L or finite depth wavenumbers vL The wavenumbers are nondimensionalized by the length L ULEN and defined relative to the gravitational acce
306. ing nonlinear motions in the tank is presented in Reference 26 The tank geometry is defined in the same manner as for the exterior surface of each body using either the low order or higher order method In both cases it is essential that the normal vector points away from the wet side of the tank surface as explained in Section 6 1 ILOWHI 0 and Section 7 1 ILOWHI 1 In the context of a tank this means that the positive normal vector points out of the tank and into the space exterior to the tank In the low order method the tank panels are included with the conventional body panels in the GDF file In the higher order method the tank patches are defined in the same manner as the body surface using one of the options listed in Sections 7 5 7 9 In both cases the tank panels or patches are identified by their starting and ending indices which must be listed in the configuration files using the parameter NPTANK as explained in Section 4 7 TEST 22 is an example where the body is an FPSO containing two rectangular internal tanks Patches 1 7 represent the exterior surface of the FPSO patches 8 11 represent tank 1 and patches 12 15 represent tank 2 When IRR 1 this convention is modified with patches 8 10 used for the interior free surface of the FPSO and patches 11 18 used for the tanks as explained in the header of the GEOMXACT DLL subroutine FPSOINT One side of each tank is represented by four rectangular patches with their vert
307. int in the order listed in the bpi input file and bpo output file The file gdf pnl is only output when IOPTN 5 gt 0 and IPNLBPT 0 If ILOWHI 1 the data output in this file differ from those shown above as follows K Index for points on the body surface See Section 5 5 XCT YCT ZCT Dimensional global coordinates of points AREA Product J U V where J is the Jacobian at the point and dU V denote the differential increments between points in parametric coordinates Ne Ny Nz Components of the unit vector normal to the body surface at each point r x n r x n r x n Components of the cross product of the position vector at each point In Option 8 the mean force and moment are output only for modes I 1 2 and 6 corresponding to the two horizontal forces and yaw moment respectively In Options 7 and 9 the six components of the mean forces and moments F are output on the first six lines with positive indices i 1 2 6 These are the components of the force and moment vectors defined with respect to the inertial reference frame corresponding to the mean position of the body coordinate system When IRAD gt 0 three additional components of the moment F are output and identified by negative indices i 4 5 6 These are the components of the moment about the moving origin denoted by o in Figure 15 1 In all cases the components of the vector force and moment are defined with respect to the inertial mean
308. ions when walls are present Only the wetted surface of the body should be paneled and then only half or a quarter of it if there exist one or two planes of symmetry respectively This also applies to bodies mounted on the sea bottom or on one or two vertical walls The number of panels NPAN refers to the number used to discretize a quarter half or the whole body wetted surface if two one or no planes of symmetry are present respectively 6 5 The displaced volume of the structure deserves particular discussion Three separate algorithms are used to evaluate this quantity as explained in Section 3 1 Except for the special case where the structure is bottom mounted the three evaluations VOLX VOLY VOLZ should be identical but they will generally differ by small amounts due to inaccuracies in machine computation and more significantly to approximations in the discretization of the body surface A general purpose pre processor has been developed for preparation of GDF files using the MultiSurf geometric modelling program 1 AeroHydro Inc 54 Herrick Rd Southwest Harbor Maine 04679 USA 207 244 4100 www aerohydro com 6 6 6 2 USE OF THE SOURCE FORMULATION ISOR 1 This section describes the evaluation and use of the source strength in the context of calculating the fluid velocity components on the body and the mean drift force and moment based on pressure integration in uni and bi directional waves In order to evalua
309. is nonuniform in this strip to give a finer discretization near the corners There are four patches on the end 4 patches on the side and 4 patches on the bottom The interior free surface is represented by patch 13 if IRR 1 CCYLHSP defines the first quadrant of a vessel with semi circular sections and horizontal axis The vessel can be sub divided into separate segments to permit the analysis of a hinged structure using generalized modes The ends of the vessel are spheroidal The vessel has two planes of symmetry ISX ISY 1 NSEG is the number of segments including cylindrical elements and the two spheroidal ends The array XSEG defines the X coordinate of the end of each segment location of joints between adjacent segments The array XSEG must be of dimension NSEG 1 2 If NPATCH NSEG 1 2 only the submerged portion of the body is represented with one patch for each segment if 7 23 NPATCH NSEG 1 2 2 the interior free surface is also represented by the last two patches the first is a rectangle covering the interior of all the cylinders and the second is a semi ellipse covering the interior of the spheroidal end Note that in accordance with FORTRAN convention NSEG 1 2 is defined as the integer part of this fraction CIRCCYL MULTI defines an array of circular cylinders with the radius draft and coordinates XC YC of the axis input separately for each cylinder The GDF parameter NCYL is the total number of cylinders defined
310. isions have been made to replace scratch files on the hard disk by arrays in RAM up to the limit of RAM that is available This can save substantial computing time To fully utilize this capability the user should assign the parameter RAMGBMAX in the configuration file as described in Section 4 7 based on the estimated amount of RAM that is not required for other purposes Some experience may be required to determine this input For a system that is not used concurrently for other substantial computations a suggested estimate is one half of the total RAM if the RAM is less than 2 Gb or the total RAM minus 1 Gb for systems with more than 2 Gb For systems running under Windows the total RAM is displayed by the Control Panel System option It is important not to assign a value of RAMGBMAX that is too large since this may result in paging or transfer of data to virtual memory on the hard disk which will slow down the computations The parameter RAMGBMAX is based on the available memory of the system and is not dependent on the inputs to each run Thus it is recommended to assign RAMGBMAX in the file config wam and not in the configuration file runid cfg associated with a particular run If RAMGBMAxX is not assigned in the configuration files the default value 0 5 is used An estimate of the actual RAM used for each run is shown in the output file wamitlog txt 14 6 Figure 14 1 RAM required for storage of the real and complex
311. itude 2A It also is possible to replicate the present results with the NBODY option specifying two independent hulls in place of the rigid constraint implied by the catamaran The figure below shows the catamaran configuration or equivalently the original hull plus its image with respect to the wall Input file test04 cfg TESTO4 POT Barge near wall ILOWHI 0 ilowgdf 1 ipltdat 5 ISOR 1 ISOLVE 0 ISCATT 0 ILOG 0 IRR 0 MONITR 0 NUMHDR 1 IWALLYO 1 Input file test04 pot TESTO4 POT Barge near wall ILOWHI 0 zi HBOT o 0 IRAD IDIFF 3 6 7 8 1 0 0 1 NBODY test04 gdf 0 12 0 0 1 O 1 0 1 0 First 10 lines of input file test04 gdf TESTO4 GDF Barge near wall ILOWHI 0 40 00000 9 806650 1 0 ISX ISY 640 3 920686 10 00000 0 3806022 0 0000000E 00 10 00000 0 3806022 0 0000000E 00 10 00000 O 0000000E 00 3 920686 10 00000 O 0000000E 00 3 920686 10 00000 1 464466 0 0000000E 00 10 00000 1 464466 Input file test04 frc TESTO4 FRC Barge near wall ILOWHI 0 1 1 1 1 0 0 0 0 3 0 20 00000 0 000000 0 000000 0 000000 5 000000 0 000000 0 000000 0 000000 20 00000 0 0 A 5 MULTIPLE BODIES TEST05 The NBODY option described in Chapter 7 is illustrated in this test run Body one is a circular cylinder of radius 1 meter and draft 2 meters Body 2 is a spheroid of length 4 meters and maximum radius 0 25 meters The gap between these two bodies is set equal to the beam of the sph
312. ity IPERIN 1 POT file contains wave periods in seconds IPEROUT 1 Output files contain wave periods in seconds IPLTDAT 0 do not output data for plotting geometry IPNLBPT 1 evaluate body pressure at points specified in body coordinates IOUTFNAME 2 output filename frc includes serial number _NN IOUTLOG 1 copy wamitlog txt file to frc_log txt file IPOTEN 1 run the POTEN subprogram IQUADI 4 inner Gauss quadrature order in higher order method IQUADO 3 outer Gauss quadrature order in higher order method IREADRAO 2 input modified RAO s from external file IRR 0 do not use irregular frequency removal ISCATT 1 Solve for scattered potential ISOLVE 2 Use two blocks in iterative solver ISOR 1 solve for source strength ITANKFPT 1 input field points in internal tanks with special format ITRIMWL 1 Trim waterlines as specified by XTRIM IWALLXO 1 the plane X 0 is a reflecting wall IWALLYO 1 the plane Y 0 is a reflecting wall KSPLIN 3 Use 3rd order B splines for potential in higher order method MAXITT 35 Maximum number of iterations in solver MAXMIT 8 Maximum number of iterations in momentum integral MODLST 1 Outputs in same order as left hand sides MONITR 1 display all FORCE output to monitor NCPU 2 Use 2 dual core processors in parallel NEWMDS 0 No generalized modes NFIELD_LARGE 0 evaluate field outputs in period loop NMODESFSP 1 Use one FSP mode NOOUT 111101111 output all but bod
313. ity name float index value For example if Point draft_pt is a point whose Z coordinate its third floating point data value controls the draft of the moda the parameter line draft pt 3 35 5 sets the draft to 35 5 Obviously carelessly setting parameters can break the MultiSurf geometry For example the leg radius and pontoon radius for a TLP might be separate parameters As long as the pontoon radius is smaller than the leg radius the geometry works but if pontoon radius is set larger than the leg radius a projection will fail and the pontoon surface can t be evaluated This failure will be reported in RGKLOG TXT If you try the same settings in MultiSurf you can see what goes wrong Even when all surfaces evaluate geometrically there can be modeling problems that affect the WA MIT solution When the pontoon radius is somewhat smaller than the leg radius it s possible for the two pontoons arriving at the leg to intersect each other which may or may not cause a recognizable error condition in WAMIT Itis thus a good idea to check all parameter combinations that you plan to use visually in MultiSurf before starting the WAMIT solutions 4 15 Patch types and color coding WAMIT recognizes several types of surface patches with different characteristics for analysis In the RG2WAMIT interface these patch types are distinguished by color coding assigning specific colors to surfaces to designate different patch types as
314. ive values of the density must not be assigned RHOTANK is only used in the FORCE run and may be changed if separate FORCE runs are made using the same POTEN outputs Further details and examples are given in Section 12 1 SCRATCH_PATH is the path designating a directory folder for storage of some scratch arrays If this input is not used all scratch storage is in the default directory where the program is run If a different directory is specified about half of the scratch arrays will be stored in the default directory and the remaining arrays will be stored in the designated alternative directory This option permits users with two or more disk drives to distribute the scratch storage thereby increasing the usable disk storage The maximum length of the pathname is 40 characters Spaces cannot be used in the pathname The example below illustrates this option This option was more useful for older systems with limited memory and disk size On contemporary systems it is less useful especially if the size of RAM is sufficiently large to store all of the temporary arrays as discussed in Chapter 14 TOLFPTWL is the tolerance used to check for field points that are close to are inside the waterline s See Section 4 3 The default value is 1078 TOLGAPWL is the tolerance used to neglect gaps between waterline panels or patches when tracing the waterline s in conjunction with automatic representation of the interior free surface Chapter 10 a
315. ixed without re running POTEN Body motions in incident waves In this case IRAD and IDIFF are set equal to 0 body free only in specified modes or 1 body free in all modes Body motions are obtained from the solution of the equations of motion using Option 4 The resulting field data and drift forces are evaluated for this particular combination of the radiation and diffraction solutions For bodies with one or two planes of symmetry ISX 1 and or ISY 1 the solution of the diffraction problem is decomposed into symmetric and antisymmetric components If IDIFF 1 all of these components are computed but if IDIFF 0 only the modes needed to evaluate the exciting forces corresponding to nonzero elements of the index IMODE in the POT file are computed Special attention is necessary when computing the pressure fluid velocity and drift forces Options 5 9 since these generally require all components of the diffraction solution To ensure a complete solution IDIFF 1 should be used in the POT file whenever Options 5 9 are computed As explained in Section 5 8 a warning message is issued if IDIFF 0 and IOPTN I gt 0 for I 5 9 stating that the solution is non physical In special cases where the heading angle coincides with a plane of symmetry the complete 4 15 diffraction solution is symmetric and it is not necessary to compute the antisymmetric component In such cases the warning message can be ignored This shortcut is illustrated
316. j 4 5 6 3 3 EXCITING FORCES a Exciting forces from the Haskind relations Xi iwp I nie ae dS b Exciting forces from direct integration of hydrodynamic pressure X iwp ff nippds So _ X GAL where m 2 for i 1 2 3 and m 3 for i 4 5 6 The separate Froude Krylov and scattering components of the exciting forces can be evaluated using the options IOPTN 2 2 and IOPTN 3 2 as described in Section 4 3 The Froude Krylov component is defined as the contribution from the incident wave po tential yo and the scattering component is the remainder Using the Haskind relations these two components correspond respectively to the contributions from the first and sec ond terms in parenthesis in the equation above Using direct integration they correspond to the components of the total diffraction potential yp in equation 15 8 3 4 3 4 BODY MOTIONS IN WAVES Two alternative procedures are followed to evaluate the body motions in waves corre sponding respectively to the Alternative 1 Section 4 3 and Alternative 2 Section 4 4 FRC control files In Alternative 1 which is restricted to a body in free stable flotation without external constraints the following relations hold m pv Ly Lg Yo Yg where m is the body mass and 4 Yg Zg are the coordinates of the center of gravity The inertia matrix is defined as follows m 0 0 0 MZ MYz 0 m 0 MZzq 0 Mg 0 0 m MYg MT 0 M o 3 3 0
317. l to 43 125 meters which corresponds to half of the distance between the centers of adjacent columns Only head seas are considered with 5 0 specified in the pot file For this reason only the modes surge heave pitch are analyzed with IRAD IDIFF 0 and these modes are specified on line 3 There is a warning message for options 5 9 as explained in Section 10 1 since IDIFF 0 In the fre file the horizontal modes 1 2 6 are free and the vertical modes 3 4 5 are fixed to represent a TLP moored by vertical tendons The Alternative 1 form is used with the result that the body mass is evaluated as if the TLP is freely floating see Section 3 5 The output shows the conventional response amplitude operator for surge and the wave loads for heave and pitch Input file test06 cfg TESTO6 CFG ISSC TLP coarse discretization ipltdat 1 ISOR 1 ISOLVE 4 ISCATT 1 ILOG 0 IRR 0 MONITR 0 NUMHDR 1 IALTFRC 2 Input file test06 pot TESTO6 POT ISSC TLP coarse discretization 450 HBOT o 0 IRAD IDIFF 3 5 10 15 1 O 1 NBODY test06 gdf 0 0 0 0 1 O 1 0 1 0 First 10 lines of input file test06 gdf TESTO6 GDF ISSC TLP coarse discretization 43 125 9 80665 1 1 128 49 09267 37 15733 0 00000 49 09267 37 15733 5 12567 51 56456 43 12500 5 12567 51 56456 43 12500 0 00000 49 09267 37 15733 5 12567 49 09267 37 15733 17 50013 Input file test06 frc TESTO7 FRC ISSC TLP ILOWHI 0 f
318. ld pressures velocities free surface elevations and drift forces follow from the corresponding Options 5 9 Note that in the default case the pressures velocities and drift forces are not separated according to each mode and the consequence of setting more than one mode to be nonzero is to superpose all such modes with unit amplitude For example if IRAD 1 and IDIFF 1 the default outputs from options 5 9 correspond to unit amplitudes of motion in all six degrees of freedom with the same phase Generally this is a nonphysical problem and care should be taken to avoid it The simplest procedure to evaluate these outputs for each mode is to set MODE I 1 for only one mode However this requires a separate run of WAMIT for each mode It is possible to output separate results for options 5 6 for each mode of forced motion in a single run using the configuration parameters INUMOPT5 INUMOPTO as explained in Section 4 7 Diffraction of incident waves by a stationary structure the diffraction problem In this case the radiation index IRAD should be set equal to 1 To solve the complete diffraction problem set IDIFF 1 with corresponding outputs from the Options 3 5 6 7 8 9 in FORCE If IOPTN 4 0 and IDIFF 1 it is assumed that the body is stationary irrespective of IRAD Thus after a complete WAMIT run where the P2F file is output from POTEN and saved it is possible to execute another run using only FORCE with the body motions both free and f
319. ld be noted are as follows e If the old configuration file uses the default name config wam a new configuration file fnamewam cfg is generated where fnamewam is the filename of the fnames file In this case a new fnames file is generated including the name of the new cfg file e In cases where IALTPOT 1 is used for the old files and the gdf file name is included in the wam file this filename is removed in the new wam file e Configuration parameters which are no longer used are removed from the new cfg file e If the same input file is used with more than one fnames file in the directory the new input file with the same name may not be correct except for the last run processed The following example illustrates how this problem may occur if two runs with fnames files RUNA WAM and RUNB WAM use the same POT file RUNAB POT with IALTPOT 1 format in V6 4 and with different GDF files RUNA GDF and RUNB GDF assigned in RUNA WAM and RUNB WAM if V6V7inp processes RUNA first and RUNB second there is only one new file RUNAB POT with the gdf file specified as RUNB GDF in this file The program V6V7inp is intended to work for all input files which were valid in Version 6 but it is impossible to test the program with all possible combinations of inputs Users are advised to check the changes in the new input files especially if error messages are generated in the WAMIT runs using these files and to report problems by email to info wamit com A
320. leration g GRAV Both ULEN and GRAV are input in the GDF file The following 4 8 table gives the definitions of each input and the corresponding value of IPERIN IPERIN Input Definition 1 Period in seconds T 2 Frequency w 2r T 3 Infinite depth wavenumber KL w L g 4 Finite depth wavenumber vL vLtanhvH w L g If the fluid depth is infinite HBOT lt 0 K v and there is no distinction between the inputs for the last two cases The default case IPERIN 1 is assumed if IPERIN is not specified in the configuration file The corresponding parameter IPEROUT controls the same perameters in the output files as explained in Section 4 7 The limiting values of the added mass coefficients may be evaluated for zero or infinite period by specifying the values PER 0 0 and PER lt 0 0 respectively Likewise the limiting values of the body pressure and velocity and the field pressure and velocity due to the radiation solution may be evaluated see Section 3 9 These special values can be placed arbitrarily within the array of positive wave periods These special values are always associated with the wave period irrespective of the value of IPERIN and the corresponding interpretation of the positive elements of the array PER For example the effect of the parameter IPERIN 2 and the array PER with the four inputs 0 0 1 0 2 0 1 0 is identical to the default case IPERIN 1 with the array PER equal to 0 0 27 7 1 0 If the irregular freq
321. les Users should refer to Chapter 4 for a complete explanation of the data in these files A few simple modifications will be outlined here for tutorial purposes in the context of Test Run 01 Before proceeding further check that the file fnames wam corresponds to this test run or re copy test01 wam to fnames wam following the instructions in Section 2 4 As the first modification we might request FORCE to perform additional computations for the same periods and wave headings analyzed by POTEN but with modified values of the vertical center of gravity VCG and radii of gyration XPRDCT in the force control file test01 frc In the standard file VCG 0 0 center of gravity in the waterplane and the radii of gyration are set equal to 1 0 the three diagonal elements of the XPRDCT matrix A positive VCG will move the center of gravity above the waterplane reducing the pitch roll hydrostatic stability and affecting these RAO s in longer wave periods Modifying the radii of gyration should change the same RAO s primarily at shorter wave periods It is not necessary to re run POTEN in this case provided the file test01 p2f has been retained for the POTEN output To avoid the extra run time of POTEN add the line IPOTEN 0 to the configuration file test01 cfg See Section 4 7 and also the file test17b cfg which includes the same line After modifications are made to the file test01 frc it is advisable to save the modified file with a different fil
322. less the configuration parameters INUMOPT5 1 and INUMOPT6 1 are used 13 6 THEORY The fundamental relations between the time and frequency domain express the added mass coefficient A and damping coefficient B in terms of Fourier transforms of the impulse response function L t MG Aes f Lu t coswt dt 13 3 Biy w Lyt sin wt dt 13 4 The inverse transforms of 13 1 2 give complementary relations for the impulse response function I Aij w Ay o0 cos wt dw 13 5 i 2 T Bul sin wt dw 13 6 0 w T Lig Similar relations exist for the exciting forces and RAOs Define one of these quantities by the complex function X w The corresponding impulse response function is real denoted by Ki t The appropriate physical ranges are 0 lt w lt oo and oo lt t lt co Then the complex Fourier transform pairs are as follows X w f Kite dt 13 7 and 2rK t f Xiu dw 13 8 Formally since K is real X w X w and thus oO InK t A X w e XF w e dw 13 9 K t o Re X cos wt Im X sin wt dw 13 10 The Fourier transofrms 13 5 13 6 and 13 10 are evaluated by truncating the infi nite integrations at the largest value of the evaluated frequency and using Filon quadra tures to evaluate the resulting finite integrals A truncation correction is applied to 13 5 Further details regarding this procedure are given in 26 13 7 DIMENSI
323. less two adjacent vertices are coincident The latter provision permits the analysis of a triangular panel with one side in the free surface The three Cartesian coordinates of four vertices must always be input for each panel in a sequence of twelve real numbers Triangles are represented by allowing the coordinates of two adjacent vertices to coincide as in the center bottom panels shown in Figure 6 1 Two adjacent vertices are defined to be coincident if their included side has a length less than ULEN x 102 An error return results if the computed area of any panel is less than ULEN x 10 19 The input vertices of a panel do not need to be co planar WAMIT internally defines planar panels that are a best fit to four vertices not lying on a plane However it is advisable to discretize the body so that the input vertices defining each panel lie close to a plane in order to achieve good accuracy in the computed velocity potentials An error message is printed if a panel has two intersecting sides A warning message is printed if a panel is convex the included angle between two adjacent sides exceeds 180 degrees The origin of the body coordinate system may be on above or below the free surface The vertical distance of the origin from the free surface is specified in the Potential Control File The same body system is also used to define the forces moments and body motions See Chapter 5 regarding the change in reference of phase relat
324. ll be 3x 11 33 Rotational symmetry about the X or Y axis is also supported but only one axis at a time In WAMIT this would haveto be a completely submerged body positioned vertically with XBODY 3 Rotational symmetry that is incomplete precludes the use of moda level rotational symmetry In this situation the entire geometry has to be built explicitly But note the RotatSurf and CopySurf entity type often provide a highly efficient way to construct the portions that are rotationally symmetric 4 8 Fast vs Accurate evaluation RGKernd has two evaluation modes denoted Fast and Accurate In Accurate evaluation all curves and surfaces are evaluated recursively using the actual math functions that provide their definitions In Fast evaluation curves and surfaces are evaluated approximately by interpolation in a stored tabulation of the curve or surface the fineness of this tabulation is controlled by the divisions x subdivisions products Fast vs accurate evaluation is specified in the GDF file for each body see below Accurate evaluation is typically slower in some cases orders of magnitude slower this especially occurs when there are deep levels of dependency in the model and or the model involves entities requiring iterative solutions such as ProjSnakes and IntSnakes The divisions and subdivisions should have no effect on the accuracy under accurate evaluation since the tabl
325. lly it is not recommended to use significantly large MAXMIT than the default value In Option 9 the evaluation of the drift force and moment is based on integration of the pressure over the body surface using the relations in 10 and 17 as summarized in Section 15 7 3 9 In Options 7 and 9 the mean drift force and moment evaluated from pressure integration and from momentum flux on a control surface are defined with respect to the body coor dinate system Conversely the mean drift force and moment evaluated from momentum conservation in Option 8 are defined with respect to the global coordinate system 3 9 ZERO AND INFINITE WAVE PERIODS It is possible to evaluate the added mass Option 1 and also the pressure and fluid velocity Options 5 and 6 in the limiting cases of zero and infinite period or equivalently infinite and zero frequency by inputting PER 0 0 and PER lt 0 0 in the POT file see Section 4 2 This extension is particularly important in the context of evaluating the corresponding time domain impulse response functions as explained in Chapter 13 The definition of the added mass coefficients is the same as shown in Section 3 2 All other force coefficients are zero in these limits with the exception of the heave exciting force and horizontal exciting moments which tend to nonzero hydrostatic limits at zero frequency Special definitions are applied to the radiation pressure and velocity in the case of zero fre
326. loating and submerged structures WAMIT Version 6 48 which is described in a separate User Manual 29 performs the extended analysis for the second order solution in bichromatic and bidirectional waves including sum and difference frequency components Version 7 has been developed to exploit important features of contemporary computing systems especially in the PC environment For systems with relatively large random access memory RAM and with multiple processors CPUs also known as cores Version 7 is developed to take advantage of these features with substantial reductions of the computing time in many applications Another important development in this context is the 64 bit operating system which is essential for data access with large RAM The remainder of this Chapter gives a general description of WAMIT Version 7 and changes made from earlier versions Users of earlier versions should refer particularly to Sections 1 2 and 1 3 which list the changes introduced in Versions 7 0 and 7 1 A mark in the left margin as on this line is used throughout this User Manual to call attention to changes in Version 7 0 WAMIT includes options to use either the traditional low order panel method or a more versatile higher order method based on B splines The description and use of WAMIT for both the low order and higher order methods of solution has been unified as much as possible Most of the input and output files are generic appli
327. ls must be identified with the parameters IWALLXO IWALLYO in the CFG file as explained in Section 12 4 The older alternative to assign negative values of ISX ISY in the low order GDF file is not supported e The option IALTFRC 2 used to specify the format and data in the FRC file must be input in the configuration files The older alternative to add an extra line in the FRC file is not supported e Two optional configuration files can be used as explained in Section 4 7 Several con figuration parameters which are no longer used have been removed including IALT POT ICTRSURF IDIAG IQUAD MAXSCR IPERIO Several new parameters are included as explained in Section 4 7 The array XBODY is required in the POT file and must not be in the CFG file e The F2T utility described in Chapter 13 is modified in accordance with the new extensions of the numeric output files The utility program v6v7inp exe is supplied with Version 7 0 to facilitate the con version of old input files from Version 6 to Version 7 Special instructions for using this 4 5 program are in Appendix B This program is intended to work for all input files which were valid in Version 6 However it is impossible to test the program with all possible combinations of inputs Users should verify the changes made by the utility especially if error messages occur running the new files 4 6 4 2 THE POTENTIAL CONTROL FILE The POT file is used to input various parameters
328. lt HBOT must be imposed if NPATCH gt 1 Figure 7 3 illustrates the patch numbering to achieve this flexibility Figure 7 3 One quadrant of the cylinder shown in Figure 7 1 showing the patch numbering system which permits using the subroutine CIRCYL with NPATCH 1 bottom mounted caisson NPATCH 2 floating cylinder of finite draft or NPATCH 3 floating cylinder with a patch on the interior free surface to remove irregular frequency effects The view is from above the free surface looking toward the interior of the cylinder Other subroutines are also included in GEOMXACT F to define a variety of bodies in all cases with IGDEF lt 0 so that positive values of IGDEF gt 2 are reserved for users 33 body subroutines are included in the standard release of GEOMXACT F and GEOMX ACT DLL as listed in the table below and explained in detail here Several of these are used for the higher order Test Runs described in Appendix A In addition there are 4 control surface subroutines in the standard release of GEOMXACT which are described in Chapter 11 The following table lists the 33 body subroutines which are described in more detail below IGDEF SUBROUTINE NPATCH GDF INPUTS 1 CIRCCYL 128 RADIUS DRAFT INONUMAP 2 ELLIPCYL 1 2 3 A B DRAFT 3 SPHERE 1 2 RADIUS INONUMAP 4 ELLIPSOID 1 2 A B C 5 BARGE 12 34 HALFLENHALFBEAM DRAFT 6 BARGEMP 6 7 HALFLEN HALFBEAM DRAFT XMP YMP 7 CYLMP 3 4 RADIUS DRAFT RADMP INONUMAP 8 TORUS 1 2 RCIRC
329. m TiMIT 13 1 DEFINITIONS OF RADIATION AND DIFFRACTION OUTPUTS The outputs from WAMIT and F2T are considered to be of either the radiation or diffrac tion type depending on whether they are caused by forced motions in calm water or by incident waves respectively The simplest physical distinction between these two types is in terms of the incident wave amplitude if the response is proportional to the wave amplitude it is of the diffraction type and vice versa The added mass and damping coefficients Option 1 are of the radiation type whereas the exciting forces and RAO s Options 2 3 4 are of the diffraction type Except as noted in Section 13 5 the pressures and fluid velocities on the body Option 5 and in the fluid Option 6 are of the diffraction type since these are defined in the WAMIT convention as total responses with the body free to respond or fixed in incident waves An important difference between the two types of outputs is in terms of their limits at infinite frequency or zero period In this limit the radiation outputs are generally real and nonzero corresponding to the added mass pressure and fluid velocity induced by forced motions of the body without wave effects on the free surface Conversely in the same limit there are no diffraction effects since the incident waves have vanishingly small wavelength and cause no disturbance of either the body or the fluid The principal radiation IRFs correspond to
330. m the file test24_xhinge dat as described in Section 9 3 This input file specifies the symmetry index ISX 1 number of segments and the x coordinates of the hinges The last cylinder and the spheroidal end are considered to be rigidly joined Thus there are five active segments corresponding to the parameter NSEG in the file and NEWMDS 4 is assigned in the TEST24 POT file In the TEST24 FRC file the 10x10 matrix of inertia coefficients is specified No external damping or stiffness matrices are input corresponding to the situation where the hinges are ideal without friction or other mechanical constraints Further information can be found in the headers and comments of the subroutines which are used to generate the geometry and to represent the hinge modes aa Ca O Figure A 2 Generalized modes used for the hinged barge with four hinges The modes on the left are tent functions suitable for use when ISX 0 When ISX 1 each mode must be either symmetric or antisymmetric as shown in the right column The latter modes are used for TEST24 The conventional rigid body modes in heave and pitch represent the nonzero vertical motions at the two ends Input file test24 cfg TEST24 CFG segmented vessel with 7 segments and 4 hinge modes ipltdat 5 ILOWHI 1 IALTFRC 2 ISOLVE 1 IQUADI 4 IQUADO 3 KSPLIN 3 MONITR 0 NUMHDR 1 IGENMDS 22 NEWMDS 4 Input file test24 pot TEST24 segmented vessel with 7 segments and 4
331. med condition as explained in Section 12 2 ZTANKFS is the real array used to specify the free surface elevations in internal tanks The data in the array ZTANKFS must be input in the same order as the data in the array NPTANK Multiple lines of this parameter may be used with an arbitrary number of data on each line but each line must begin with ZTANKFS If the array ZTANKFS is included it must include one real number for each tank If the array ZTANKFS is not included the waterline of each tank is derived from the highest vertex of the GDF inputs ZTANKFS is only used when the waterline trimming parameter ITRIMWL 1 Further information is given in Section 12 1 The syntax of the configuration file is illustrated in the following example To specify each of the desired inputs the corresponding parameter is displayed followed by an sign followed by the value of the parameter These lines may be in any order Lines which do not contain an sign are ignored Comments may be inserted following the value of a parameter on the same line separated by at least one blank space Since a blank space is used to designate a comment the names of directories or folders in SCRATCH PATH and USER_PATH cannot include blank spaces All elements of the arrays NOOUT 9 and XBODY 4 should be displayed in order on one line for the sake of readability Lines which start with any characters other than the explicit parameters shown below are ig
332. mes IF block ends if IRAD gt 1 and IDIFF gt 1 IF block starts if IDIFF gt 1 Loop over wave headings starts NBETA times Loop over number of symmetric images repeat MXNLHS times Loop over number of patches repeat NPATCH times WBD I M NB I NP 1 NQ omit if IFLAT L 1 End of the loop over number of patches End of the loop over symmetric images Loop over wave headings ends NBETA times IF block ends if IDIFF gt 1 IF block ends if IFREQ 0 IF block starts if IRAD gt 1 Loop over left hand side starts repeat NLHS times Loop over number of modes for each left hand side 5 6 MDI mode index Loop over number of symmetric images repeat MXNLHS times Loop over number of patches repeat NPATCH times WBR I ICOL MDI I NP 1 NQ omit if IFLAT L 1 End of the loop over number of patches End of the loop over symmetric images End of the loop over number of modes for each left hand side Loop over left hand side ends repeat NLHS times IF block ends if IRAD gt 1 End of the loop over number of periods NP 1 and NQ are the pointers of the first and the last B spline coefficients of the unknown velocity potential on patch L HLINE header line ISX ISY Symmetry index 1 0 symmetric asymmetric ULEN Characteristic length specified in GDF NPATCH Number of patches IRAD IDIFF Radiation diffraction problem indices NPER NBETA Number of periods and wave headings NEQN The total number of unkno
333. meter may be used with an arbitrary number of data on each line but each line must begin with RHOTANK The total number of tanks NTANKS is derived from the inputs NPTANK in the POTEN run If fewer than NTANKS values of RHOTANK are specified the remainder of the array is assigned the last non negative value Thus if the density is the same for all tanks only the first value is required Zero may be assigned but negative values of the density must not be assigned RHOTANK is only used in the FORCE run and may be changed if separate FORCE runs are made using the same POTEN outputs The following are equivalent formats for the required lines in the file TEST22 CFG NPTANK 8 11 12 15 patch panel indices for two tanks RHOTANK 0 6 0 6 fluid densities for tanks one and two NPTANK 8 11 patch panel indices for tank one NPTANK 12 15 patch panel indices for tank two RHOTANK 0 6 These examples illustrate the following rules 1 Only integer data are recognized in NPTANK Arbitrary ASCII characters other than these can be used both as comments and to delimit the pairs of indices for each tank according to the user s preferences At least one blank space must be used to separate pairs of indices Comments appended to these lines must not include integer characters 2 The total number NTANKS of tanks to be included is determined by the number of pairs of indices in NPTANK inputs in this case NTANKS 2 The same number of de
334. mitted in the figures below to show more clearly the bottom and the side of the moonpool To clarify the behavior near resonance the wavenumber K is input in the POT file with the corresponding option IPERIN 3 specified in the TEST17 cfg file 61 values of K are input in the range 0 1 lt K lt 1 5 to describe the behavior near resonance The computed hydrodynamic parameters include the force coefficients RAO s and the elevation of the free surface at the center of the moonpool When the structure is fixed in heave the resonant pumping mode in the moonpool occurs at Kd 0 85 The outputs related to the vertical force component display singular features near this point This includes large amplitudes of the heave damping and exciting force and negative added mass The heave RAO has two adjacent resonant peaks as shown in the Figure below due to coupling between the heave mode and the moonpool pumping mode Test17 Testi7a Test17b tm am Test17 c Test17 bh Test17 bq RAO3 Figure A 1 Heave RAO for each of the test17 runs The results for Test17 Test17a and Test17c are practically identical The results for Test17b lid with damping include three values of the external damping coefficients In Test17b b33 0 4 and b77 0 1 as shown in the test17b frc file below In Test17bh these values are reduced by a factor of one half and in Test17bq they are reduced by a factor of one quarter These very large responses are non physi
335. modes physically analogous to pitch and heave but defined relative to the body are introduced via the subroutine MOONPOOL_FS in NEWMODES F In test run TEST17a the lid is assumed to be free with no external force or moment acting on it The IALTFRC 2 option is employed and the only external force matrix that is included in TEST17 FRC is the mass matrix of the body This mass matrix is equivalent to the radii of gyration specified in TEST17 FRC It can be confirmed by comparison of the outputs that the motions of the body RAO are virtually identical to TEST17 as shown in the Figure above confirming that the representation of the moonpool free surface in this manner is legitimate A comparison can also be made between the moonpool free surface elevation numeric output file TEST17 6 and the response of the lid in mode 7 RAO 7 in the numeric output file TEST17a 4 but in this comparison account must be made for the fact that RAO 7 is relative to the body motions and thus it is necessary to compare the complex sum RAO 3 RAO 7 in TEST17a with the moonpool free surface elevation in TEST17 The input file test17a pot uses the optional parameter NPERGROUP to define the same array of wavenumbers as in test17 pot in a more compact manner as described in Section 4 2 In TEST17b empirical damping is introduced via the external damping matrix in TEST17b FRC Since this is the only difference between TEST17a and TEST17b it is not necessary to re
336. mples are explained below for TEST23 and TEST24 IERROR is the unit number assigned by WAMIT for the log files ERRORP LOG and ERRORF LOG which are described in Section 10 1 Error messages which are generated in DLL subroutines can be added to the error files ERRORP LOG and ERRORF LOG by using the file number IERROR IWAMLOG is the unit number assigned by WAMIT for the log file WAMITLOG TXT This unit number can be used to copy the special input data file to the log file as is done for other input files by WAMIT The use of this procedure with a special input data file is illustrated in TEST16 TEST18 TEST23 and TEST24 In TEST16 the subroutine FREEBEAM_X is used to represent the bending modes and the length of the beam is input from the special file test16 Length dat In TEST18 the subroutine JACOBI is used to represent the cantilever bending modes with shifted Jacobi polynomials and the depth of the column is input from the special file test18_depth dat In TEST23 the subroutine WAVEMAKER inputs the depth of the hinge axis from a special file test23_wmkrhinge dat In TEST24 the subroutine HINGE MODES inputs data from the file test24_xhinge dat Users who modify the DLL subroutines or make new DLL subroutines can follow the code in these subroutines for guidance in inputting data from an external file 9 8 9 4 HYDROSTATICS To evaluate the motions of a body including generalized modes it is necessary to evaluate the corresponding hydro
337. mples showing typical WAMIT runs for a circular cylinder and for a barge Additional examples are included in Reference 24 NPATCH can be specified as 0 use of this option is recommended to avoid errors in counting surfaces or patches In this case the number of patches is evaluated from the MultiSurf model and the user does not need to input NPATCH separately If NPATCH gt 0 is input by the user the number of MultiSurf sur faces used in the solution will be limited to NPATCH thus input files for earlier versions of WAMIT can still be used without modification An import utility File Import WAMIT GDF has been added to MultiSurf to convert low order WAMIT gdf input files to ms2 geometry database files for MultiSurf Its results depend on the organization and content of the gdf file In general this utility will create correctly dimensioned points for building a surface model in MultiSurf and if the gdf file is suitably structured it is possible to create appropriate surface patches for higher order analysis with the IGDEF 2 option 1 AeroHydro Inc 54 Herrick Rd Southwest Harbor Maine 04679 USA 207 244 4100 www aerohydro com 7 12 7 8 ANALYTIC REPRESENTATION OF THE GEOMETRY This option can be used in cases where the geometry of the body can be defined explicitly with the fundamental advantage that the definition of the body geometry is exact and that the only numerical approximation which remains is in the representation
338. multiple of NCPU When NCPU gt 1 the BREAK option to interrupt the run is disabled and cannot be used See Section 4 12 14 7 MODIFYING DLL FILES The files geomxact f and newmodes f can be modified by users following the instructions in Sections 7 9 and 9 3 This makes it possible for users to develop special subroutines for the definitions of the body geometry and generalized modes respectively and to link these subroutines with WAMIT at runtime WAMIT Version 7 is compiled with Intel Visual Fortran Version 12 1 The previous Version 6 4PC was compiled with Intel Visual Fortran Version 10 1 and earlier versions were compiled with Compaq Visual Fortran Any of these Fortran compilers can be used to compile modified versions of the files geomxact dll and newmodes dl1 for use with a single processor NCPU 1 using the following procedure e Open a new project geomxact as a Fortran Dynamic Link Library Add geomxact f to the project e Build a release version of geomxact d1l Copy the new version of geomxact d11 to the working directory for WAMIT The same procedure is used for NEWMODES except for the different filenames Users who modify the DLL files for runs with multiple processors NCPU gt 1 are advised to contact WAMIT Inc for special instructions It may be possible to use other FORTRAN compilers to build the DLL files but certain conventions in calling subroutines must be consistent with those of Intel Vis
339. n XFIELD 1 n XFIELD 2 n XFIELD 3 n ITANK n is an integer which specifies the tank number containing the n th field point If ITANK n 0 the field point is in the exterior domain The numbering of the tanks corresponds to the order of the NPTANK indices as explained below The default value is ITANKFPT 0 ITRIMWL is the integer parameter used to specify the trimmed waterline option See Section 12 2 When ITRIMWL 1 the array XTRIM must be included for each body The default value is ITRIMWL 0 IWALLXO is the integer parameter used to specify that the plane X 0 is a reflecting wall See Section 12 4 When IWALLX0 1 the fluid is bounded by a reflecting wall at X 0 The default value is IWALLX0 0 IWALLYO is the integer parameter used to specify that the plane Y 0 is a reflecting wall See Section 12 4 When IWALLY0 1 the fluid is bounded by a reflecting wall at Y 0 The default value is IWALLYO 0 KSPLIN is an integer parameter specifying the value of the B spline orders KU KV for 4 31 all patches when the higher order method is used ILOWHI 1 The default value is KSPLIN 3 See Sections 7 11 12 for further information MAXITT is an integer parameter used to specify the maximum number of iterations in the iterative solver See Section 14 2 The default value MAXITT 35 is recommended for general use MAXMIT is the maximum number of iterations in the adaptive integration used to evaluate the momentum integral for th
340. n Chapter 10 The geometry and most other inputs are the same as in TESTO1 The parameter IRR 3 is set to use automatic panelization of the interior free surface Wave periods are chosen so that the wave frequencies are near the first and second irregular frequencies of the cylinder The direct solver ISOLVE 1 is used since the iterative and block iterative solvers do not converge reliably for the source formulation ISOR 1 The GDF input is the same as TESTO1 GDF The additional panels on the interior free surface which are generated automatically by the program are shown in red in the Figure below Input file test02 cfg TESTO2 CFG Circular cylinder ILOWHI 0 IRR 3 direct solver ilowgdf 1 ipltdat 5 IRR 3 ISOR 1 ISOLVE 1 ILOG 1 MONITR 0 NUMHDR 1 Input file test02 pot TESTO2 POT Circular cylinder ILOWHI 0 IRR 3 i HBOT Le IRAD IDIFF 2 1 182288 1 003025 1 0 0 1 NBODY test02 gdf 0 0 0 0 0 0 0 0 1 1i 1 ds 1 First 10 lines of input file test02 gdf TESTO2 GDF circular cylinder R 1 T 0 5 ILOWHI 0 IRR 3 1 000000 9 806650 1 1 256 0 0000000E 00 0 0000000E 00 0 5000000 0 0000000E 00 0 0000000E 00 0 5000000 0 1243981 1 2252143E 02 0 5000000 0 1250000 0 0000000E 00 0 5000000 0 1250000 0 0000000E 00 0 5000000 0 1243981 1 2252143E 02 0 5000000 Input file test02 frc TESTO2 FRC Circular cylinder ILOWHI 0 IRR 3 1 1 1 1 0 3 0 1 J 0 000000 1 000000 0000000 0000000 00
341. n the following format OPTN 1 PER I J Ai Bi OPTN 2 PER BETA I Mod X Pha X Re X Im X OPTN 3 PER BETA I Mod X Pha X Re X Im X OPTN 4 PER BETA I Mod Pha amp Re Im amp OPTN 5P PER BETA M K Mod p Pha p Re p Im p OPTN 5VX PER BETA M K Mod V Pha V Re V Im V OPTN 5VY PER BETA M K Mod V Pha V Re V Im V OPTN 5VZ PER BETA M K Mod V Pha V Re V Im V OPTN 6P PER BETA L Mod p Pha p Re p Im p OPTN 6VX PER BETA L Mod V Pha V Re Vz Im V OPTN 6VY PER BETA L Mod V Pha V Re V Im V OPTN 6VZ PER BETA L Mod V Pha V Re V Im V OPTN 7 PER BETA BETA I Mod F Pha F Re F PER BETA BETA I Mod Fi Pha Fio Re Fo OPTN 8 PER BETA BETA I Mod F Pha F Re F OPTN 9 PER BETA BETA I Mod F Pha F Re F PER BETA BETA I Mod Fi Pha Fi Re Fio Depending on the value of NUMNAM the filenames OPTN are replaced by frc as a in Section 4 7 All output quantities are nondimensionalized as defined in Sections 3 2 8 Complex quantities are defined by the magnitude Mod phase in degrees Pha and also in terms of the real Re and imaginary Im components The phase is relative to the phase of an incident wave at the origin of the global coordinates system If Option 5 is specified and INUMOPT5 1 the numeric output files 5p 5vx 5vy 5vz contain the separate components of the radiation and diffraction pressure and velocity in the
342. names including JR followed by the same extensions as the WAMIT output files The second set have the appended filenames including _JR The first set follow the same format as the WAMIT numeric output files of the same number except that the period is replaced by the time step and the WAMIT force coefficients are replaced by their Fourier cosine and sine transforms Different modes and mode combinations are listed on separate lines with the identifying mode indices just as in the numeric output files of WAMIT To facilitate plotting and separation of the different modes and wave angles BETA all of the Fourier cosine sine transforms are listed on one line in the output files denoted by _JR in the same order of mode combinations but without explicit mode indices The cosine sine transforms are listed as pairs unless one or the other is ommitted by setting IOUTFCEFS equal to 1 or 2 as explained in the following paragraph Column one of the _JR file contains the value of time t Either the cosine transforms of the added mass or the sine transforms of the damping can be used to evaluate the radiation IRFs cf equations 13 3 and 13 4 below These two sets of data can be checked to verify their accuracy and consistency in much the same way that the Haskind and Diffraction exciting forces or cross coupling coefficients are compared Alternatively to achieve more compact output files one of these transforms can be omitted using the parameter IOUTFCFS
343. nd Canada 1993 PDF C H Lee and J N Newman Second order Wave Effects on Offshore Structures BOSS 94 MIT 1994 C H Lee J N Newman and X Zhu An extended boundary integral equation method for the removal of irregular frequency effects International Journal for Numerical Methods in Fluids 23 637 660 1996 DOI C H Lee WAMIT Theory Manual Report 95 2 Dept of Ocean Engineering MIT 1995 H Maniar A three dimensional higher order panel method based on B splines Ph D Thesis Department of Ocean Engineering MIT Cambridge Massachusetts 1995 Link C H Lee H Maniar J N Newman and X Zhu Computation of wave loads using a B spline panel method Proceedings 21st Symposium on Naval Hydrodynamics Trondheim Norway 1996 Link C H Lee and J N Newman HIPAN V2 1 User Manual MIT 1999 J E Kerwin and C S Lee Prediction of Steady and Unsteady Marine Propeller Performance by Numerical Lifting Surface Theory Transactions Society of Naval Architects and Marine Engineers 86 1978 M E Mortenson Geometric Modeling Second Edition Wiley 1997 Digital Press 1999 ISBN 13 978 0471129578 M Etzel and K Dickinson Digital Visual Fortran Programmer s Guide Digital Press 1999 C H Lee J S Letcher Jr R G Mack II J N Newman D M Shook and E Stanley Integation of Geometry Definition and Wave Analyis Software OMAE 2002 Conference Oslo June 2002
344. nd automatic representation of control surfaces Section 4 3 The default value is 107 USERID_PATH designates the directory folder where the input file userid wam is stored This input file is required for users of V7PC It is convenient to store userid wam the executable wamit exe and the dynamic link libraries DLL listed in Section 2 1 together in one directory as explained in Section 2 1 In this case USERID PATH should be specified as in the example below The maximum length of the pathname is 40 characters 4 35 Spaces cannot be used in the pathname The default value of the pathname is the current directory VMAXOPTS is a real parameter which can be used to output a warning message when the nondimensional fluid velocity on the body surface exceeds this value during the eval uation of the mean drift force and moment from pressure integration on the body surface If VMAXOPT9 gt 0 at any point s used in the integration the body number panel or patch number coordinates of the point and magnitude of the velocity are output in the file wamitlog txt as explained in Section 5 6 This procedure can be used to identify points on the body surface where the representation of the body geometry may be deficient in some respect The default value is 1 0 XTRIM is the real array used to specify the trimmed waterline option XTRIM includes three real numbers specifying the vertical displacement pitch and roll of the body in the trim
345. nd earlier an Entity List was called an ObjectList This is consistent with the following general terminology conventions MultiSurf 4 amp 5 Surface Works and MultiSurf 6 object entity entity entity type support parent dependent child A simple alternative is to specify for the Entity List This will signify all visible surfaces in the model To be visible a surface has to havea positive visibility index and be on an enabled layer Surfaces that are not to be included in the hydrodynamic analysis can either be hidden by editing their visibility property or located on a layer that is disabled in the M S2 file unchecked in Settings Layers dialog Entity List ObjectList is an entity type that has been supported since MultiSurf 4 0 It is just a list of other entities of any type It is a non graphical entity you may or may not be able to see the entities in the list that depends on whether each entity is made from a graphical entity type whether it is visible and whether it is on a turned on layer But the Entity List itself is never drawn itis just a list In MultiSurf 6 and later to create an Entity List use Insert Entity List You can preselect the parents i e the entities to bein the list You can add or subtract entities just as you would edit the multiple parents of any other entity Select By Nameis often the best way to select an Entity List or find it in the Entities
346. ndex of the mode 2 the normal component of the displacement and 3 the vertical component of the displacement The symmetry indices which are defined above in the Introduction identify the symmetry of each mode assuming the body has one or two planes of symmetry by assigning the values 1 2 3 6 to indicate the same symmetries as the corresponding rigid body modes Note 9 6 that sway roll and surge pitch have the same symmetries Thus the symmetry indices 2 4 and 1 5 are redundant and either value can be assigned The normal component of the displacement denoted VELH in NEWMODES is com puted from the product of the displacement vector U V W and the normal vector XN The vertical component of the displacement denoted ZDISP in NEWMODES is identical to the component W of the displacement vector U V W Several other inputs are included in the argument list of NEWMODES to simplify its use and increase its computational efficiency These include the body index IBI the vector IBMOD which specifies the starting index for each body in the global array of mode indices the patch panel index IPP the vector NEWMDS which specifies the number of generalized modes for each body the integer IGENMDS specified in the configuration file and an integer IFLAG which specifies the required outputs from each call The inputs are explained in more detail below Unit numbers for three files are also included in the argument list to facili
347. nding inputs N and N on each patch to achieve this objective The relations between the number of basis functions and the number of panels are as follows M N hy 1 M N Ky 1 7 5 Since K K 1 in the low order panel method the number of unknowns is the same as the number of panels Chapter 6 of 18 contains examples showing how the accuracy of the solution depends on K and N for various geometries 7 3 ORDER OF GAUSS QUADRATURES Another topic which must be considered is the integration over patch surfaces Since the Galerkin method is used to solve the boundary integral equation as described in Chapter 15 this integration is carried out first with respect to the source point and then with respect to the field point These are referred to respectively as the inner and outer integrations which are carried out in parametric space For this purpose each patch is sub divided into N x N panels and Gauss Legendre quadrature is applied on each panel The orders of the Gauss quadratures are specified by input parameters Experience with a variety of applications has shown that it is sufficient to set the order of the outer integrals with respect to u v equal to Ku K and the order of the inner integrals equal to kK 1 Ko 1 7 6 7 4 THE GEOMETRIC DATA FILE In the higher order method the first part of the GDF file is as follows header ULEN GRAV ISX ISY NPATCH IGDEF Subsequent data may be included in the GDF
348. nds to read data from the GDF file appropriate code must be included in the subroutine following the examples which are contained in the original version of GEOMXACT F as delivered to the user It is important to use the attribute SAVE for any input data or intermediate data which must be preserved in the subroutine after the initial call e Users may place all of their own code in a new subroutine and name it GEOMXACT or in a subsidiary subroutine called by GEOMXACT The latter arrangement which is followed in the GEOMXACT F file distributed with WAMIT effectively produces a library of subroutines which can all be accessed by the corresponding values of the parameter IGDEF e Some or all of the geometric data may be input in a user defined file separate from the GDF file In this case standard FORTRAN coding conventions should be followed with the user s file s opened read and closed in the initial call to the GEOMXACT subroutine Unit numbers should be assigned above 300 to avoid conflicts with other open files in WAMIT The procedure for doing this is similar to that described in Section 9 3 for NEWMODES DLL In all cases the GDF file must contain at least 6 lines including the last line 0 NLINES if there is no additional data to input from the GDF file In order to use GEOMXACT for any of the purposes described in this Chapter the file GEOMXACT DLL must be in the same directory as WAMIT EXE Instructions for making new DLL files
349. ne with three possible values Initially NEWMODES is called once with IFLAG 1 to assign the array IMODE specifying the symmetry index for each mode In subsequent calls where only the normal component of the displacement vector VELH is required IFLAG 1 If both VELH and the vertical component ZDISP are required for computations of hydrostatic coefficients IFLAG 2 In the higher order method a large number of calls are made to NEWMODES with IFLAG 1 If computational efficiency is important this should be considered in modifying or extending the subroutines in NEWMODES The comments inserted in the NEWMODES file should be consulted for further details Regardless if NEWMODES is used or not the file newmodes d11 must be in the same directory as WAMIT EXE 9 7 Instructions for making new DLL files are included in Section 14 7 In some cases it is useful to input data from a special input file so that the subroutines in NEWMODES can be used with different values of relevant parameters The following arguments have been added to NEWMODES to facilitate this procedure IFILEDLL is the unit number assigned by WAMIT to open and read the special data file This unit number should be used in all cases so that there is no conflict with other files used by WAMIT for input and output FILENDLL is the filename gdf of the GDF input file gdf GDF for the same body This may be used optionally to distinguish between different special input data files Exa
350. near one or two vertical walls is described in Section 5 3 In this test run a rectangular barge of length 80m beam 20m draft 10m is positioned with its longitudinal axis parallel to one wall separated by a gap of 2m Incident head waves are considered and computations are made of the surge heave and pitch coefficients RAO s and drift force and moment in incident waves which propagate parallel to the wall BETA 0 In the GDF file one half of the barge is discretized forward of the midship section x 0 Both the port and starboard sides of the barge are included in the GDF file hence the appropriate symmetry indices for this case are ISX 1 ISY 1 Since the incident waves propagate parallel to the wall this problem is identical to the barge catamaran studied in 6 and in TEST19 the only modifications required in the latter case are 1 a lateral offset equal to the sum of the half beam and gap must be added to the y coordinates of the panels in the GDF file 2 ISY 1 and 3 the forces and moments calculated for the catamaran are the total acting on both hulls The definition of the incident wave amplitude differs between these different problems however due to the convention for the wave amplitude in the presence of a wall Section 5 3 In the present case where the incident wave angle is zero and the waves propagate parallel to the wall the wave system in the absence of the body is a progressive wave with total physical ampl
351. ng a panel are listed sequentially There are two situations when panels lie on the free surface and thus all four vertices are on the free surface 1 the discretization of a structure which has zero draft over part or all of its submerged surface and 2 the discretization of the interior free surface for the irregular frequency removal as described in Chapter 10 For the first case where the panels are part of the physical surface the panel vertices must be numbered in the counter clockwise direction when the panel is viewed from the fluid domain as in the case of submerged panels For the second case where the panel is interior to the body and non physical the vertices must be numbered in the clockwise direction when the panel is viewed from inside the structure or in the counter clockwise direction when the panel is viewed from above the free surface Details of the discretization of the interior free surface are provided in Chapter 10 Although the panels on the free surface are legitimate in these two special cases a warning message is displayed by WAMIT when it detects panels with zero draft which have four vertices on the free surface This is to provide a warning to users for a possible error in the discretization other than the above two exceptional cases The run continues in this case without interruption An error message is displayed with an interruption of the run when the panels have only three vertices on the free surface un
352. nored A convenient way to remove parameters temporarily is to add a comment character such as before the name of the parameter This is done in the example below since NPFORCE and NPNOFORCE cannot be used together for the same body In the cfg files shown in Appendix A this is done to emphasize that the header on line one is a comment The following example of a configuration file illustrates all of the possible input param eters for NBODY 1 Section 8 6 shows additional inputs for NBODY gt 1 For clarity the parameters are arranged in alphabetic order but their actual order is arbitrary IALTCSF 1 use Alternative 1 to evaluate the control surface drift force IALTFRC 1 use FRC format in Section 4 3 IBODYW 0 No wavemakers are present in walls ICCFSP 1 Include external restoring coefficients on FSP pressure surfaces 4 36 IDELFILES 1 Overwrite old P2F file without interactive input IFIELD ARRAYS 1 arrays of field point data is assigned as in Section 4 11 IFORCE 1 run the FORCE subprogram IGENMDS 1 run DEFINE subroutine in dll file for generalized modes ILOG 1 integrate the log singularity separately ILOWGDF 0 do not output low order GDF from higher order geometry ILOWHI 0 use low order method IMODESFSP 1 specifies NEWMODES subroutine to define FSP modes INUMOPT5 1 output the separate components of the body pressure velocity INUMOPT6 1 output separate components of the field pressure and veloc
353. not be used to evaluate the vertical component of the drift force Tests with larger number of panels are reported in Reference 12 to show the sensitivity of the results to the discretization of the body The vertical drift force predicted by the mean pressure integration shows slow convergence near the heave resonance frequency KL 0 66 due to cancelation between two large contributions of opposite signs the second integration in equations 12 47 and 12 48 when the heave motion amplitude is large Input file test03 cfg TESTO3 CFG Cylinder R T 1 ILOWHI 0 ISOR 1 ilowgdf 1 ipltdat 5 ISOR 1 ISOLVE 0 ISCATT 0 ILOG 0 IRR 0 MONITR 0 NUMHDR 1 Input file test03 pot TESTO3 POT Cylinder R T 1 ILOWHI 0 ISOR 1 7 14 HBOT 1 1 IRAD IDIFF 4 2 837491 2 398118 2 006409 1 638226 1 0 0 1 NBODY test03 gdf 0 0 0 0 0 515 0 0 E ae es a First 10 lines of input file test03 gdf TESTO3 GDF Cylinder R T 1 ILOWHI 0 ISOR 1 1 000000 9 806650 1 1 288 0 0000000E 00 0 0000000E 00 0 4850000 0 0000000E 00 0 0000000E 00 0 4850000 0 1934213 2 5464399E 02 0 4850000 0 1950903 0 0000000E 00 0 4850000 0 1950903 0 0000000E 00 0 4850000 0 1934213 2 5464399E 02 0 4850000 Input file test03 frce TESTO3 FRC Cylinder R T 1 ILOWHI 0 ISOR 1 0 0 0 1 0 0 0 1 1 0 000000 0 742000 0 000000 0 000000 0 000000 0 742000 0 000000 0 000000 0 000000 1 000000 0 0 A 4 BODY NEAR A WALL TEST04 The option to analyze a body
354. not necessary or desirable to use a large number of small patches on each flat surface as would be necessary to achieve accurate results with the low order method The most efficient procedure is to use the smallest number of patches which permits a complete representation of the structure For a simple rectangular barge one quadrant can be represented with three patches bottom side end If a rectangular moonpool is centered amidships 6 patches are required with two on the bottom and two on the walls of the moonpool This option also might be useful to check the accuracy of a low order application using the same GDF file for both except that IGDEF 0 must be assigned for the higher order input Two caveats should be noted in this context First since each low order panel is replaced by a patch the number of patches may be quite large this will result in substantially longer run times and memory requirements as compared with the low order method Secondly if the flat low order panels do not correspond exactly to the body surface this part of the low order approximation is not refined by such a check 7 8 7 6 GEOMETRY REPRESENTED BY B SPLINES IGDEF 1 The most general approach to represent the geometry in the higher order method is the same as that which was first developed in 18 19 In this approach each patch of the body is represented by B splines in an analogous manner to the representation of the velocity potential Section 7 2
355. nsities RHOTANK is required for the analysis but it is not necessary to input repeated values if all of the densities are the same or if all of the densities after a certain point are the same The order of the tank densities must correspond to the order of the index pairs in NPTANK 3 The data in RHOTANK are real numbers After specifying all NTANKS values arbitrary comments can be appended as in the first example above but if fewer than RHOTANK real numbers are assigned the remainder of the line should be left blank as in the second example above The real array ZTANKFS can be included in the configuration files as explained in Section 4 7 to specify the free surface elevations in internal tanks The data in this array define the elevations of the tank free surfaces above the plane Z 0 of the exterior free surface The data in the array ZTANKFS must be input in the same order as the data in the array NPTANK Multiple lines of this parameter may be used with an arbitrary number of data on each line but each line must begin with ZTANKFS If the array ZTANKFS is included it must include one real number for each tank If the array ZTANKFS is not included the waterline of each tank is derived from the highest vertex of the GDF inputs ZTANKFS is only used when the waterline trimming parameter ITRIMWL 1 as explained in Section 12 2 The data in ZTANKFS are dimensional with the same units of length as are used in the GDF file Spe
356. nsitive in Windows but are case sensitive in Linux 4 Thespecified Entity List was not found in the model file An Entity List of wetted surfaces may be specified by namein the GDF file Entity names in RG are case sensitive and must use an underscore _ in place of a space Check to see that the Entity List nameis correctly spelled and correctly capitalized in the GDF Open the M S2 file in either MultiSurf or Notepad and see that the Entity List is there and you have given its correct name in the GDF You can find the Entity List in the Entities M anager under Entity Lists or use Select By Name 5 Wetted surface Entity List has an error 10 11 The RGKernel error code will be given This is most likely to occur because one of the surfaces failed to evaluate and the Entity List got an error 284 support failed as a result If the M S2 opens in MultiSurf without error or warnings it is very likely to open and evaluate successfully in RG2WAMIT However the two RGKernel dill versions will generally be different and may have some incompatibilities so itis possible for this error to occur through no fault of the user This situation should be investigated by AeroHydro Failed to build surface table Open the MS2 filein MultiSurf and confirm that the surface in question evaluates without error If the surface evaluates without error in MultiSurf it is very unlikely to fail in RG2WAMIT However because of some incompatibilities
357. ntal forces and yaw moment because it does not include the waterline integral However Alternative 2 based on equations 15 59 and 15 60 must be used when CL is very close to the body This is because the evaluation of the momentum flux which involves the pressure and or velocity is not accurate very close to the body An example for which the Alternative 2 may be required is when the gap between two adjacent bodies is very small The evaluations of the vertical drift force and horizontal components of the drift moment are identical in these two alternative methods The option to use Alternative 1 or Alternative 2 is controlled by the parameter IALTCSF in the configuration file as explained in Section 4 7 The default value is IALTCSF 1 It is possible to use two separate control surface files to represent the inner free surface and the remaining outer portion of the control surface This procedure is described in Section 10 4 It is also possible to define the control surface automatically as described in Section 10 5 When this is possible it avoids most of the effort required to define the control surface To evaluate the mean drift forces and moments using this method the Control Surface File CSF defining the geometry of the control surface must be prepared The CSF file must have the same filename as the corresponding geometric data file for the body with the extension csf i e gdf csf The control surface must be a closed sur
358. nterior free surface and test13as spl includes the spline parameters NU NV for this extra patch Conversely for the cylinder the input files testl3ac gdf and testl3ac spl do not include the extra patch since this is added by the program using IRR 3 Input file testi3a cfg TEST13A CFG Cylinder spheroid with trim IPLTDAT 4 ILOWHI 1 IRR 1 3 IRR 2 1 ILOG 1 ISOLVE 1 KSPLIN 3 IQUADO 3 IQUADI 4 NUMHDR 1 NOOUT 0 11101111 IALTFRC 3 Alternative Form 3 FRC IALTFRCN 1 1 ITRIMWL 1 trim waterline XTRIM 1 1 0 15 0 XTRIM 2 0 0 0 0 Input file testi3a pot testi3a POT Trimmed Cylinder spheroid IRR 3 a 1 1 IRAD IDIFF 2 NPER array PER follows 1 00 2 00 1 NBETA array BETA follows O 2 NBODY testi3ac gdf 1 25 0 0 0 0 0 0 XBODY 1 1 1 1 1 1 IMODE 1 6 test13as gdf 0 5 0 0 0 0 90 0 XBODY Li de dd A S 1 IMODE 1 6 Input file testi3ac gdf testi3ac gdf Cylinder trimmed no interior fs 1 9 80665 ULEN GRAV 1 1 ISX ISY 2 1 NPATCH IGDEF 2 NLINES 1 0 2 0 RADIUS DRAFT 0 UNIFORM MAPPING Input file testi3as gdf testi3as gdf untrimmed spheroid with interior fs IRR 1 1 9 80665 ULEN GRAV 1 1 ISX ISY 2 4 NPATCH IGDEF 1 NLINES 2 0 0 25 0 25 A B C Input file testi3ac spl TEST13C cylinder R 1 T 2 analytic geometry npatch 2 8 8 NU NV side 8 4 NU NV bottom Input file testi3as spl testi3as spl untrimmed spheroid with interior fs for IRR 3 4 2 body patch N
359. nts with patches As a general rule this approach requires a large number of panel subdivisions of the patches as the thickness of the elements decreases and thus becomes inefficient The second is to reduce the thickness to zero and represent the elements by 7 1 special dipole patches analogous to the thin wing approximation in lifting surface theory 21 The procedure for defining dipole patches is described in Section 7 10 In Version 7 the dipole patches must be defined in the configuration files The alternative option in Version 6 to define the dipole patches in the GDF file is no longer supported Section 7 11 describes the optional Spline Control File SPL which can be used to define the orders of the B Splines Gauss quadratures and the numbers of panel subdivisions on each patch The maximum size of the panels measured in dimensional units can be specified in the configuration files instead of specifying the number of panels on each patch in the SPL file This is particularly convenient to achieve a panel size that is commensurate with the body dimensions and wavelength Default values of the remaining parameters in the SPL file B spline and Gauss quadrature orders are assigned automatically if not input by the user Section 7 12 describes this procedure which permits users to exploit the flexibility and efficiency of the higher order method with a minimum of inputs Section 7 13 compares the advantages of the higher ord
360. od is used ILOWHI 0 the format of the BPO file is as follows gdfBPO M Ni Ri N2 R2 N3 R3 N4 R4 Here M is the quadrant index N1 is the panel index of the nearest panel and R1 is the radial distance from the specified point x y z to the centroid of the panel Successive pairs Ni Ri are the index and radial distance to the other panel centroids where i 1 2 NNEAR NNEAR is equal to the absolute value of the configuration parameter IPNLBPT In the example shown above NNEAR 4 In the higher order method ILOWHI 1 where the solution for the velocity potential and pressure is represented by continuous B splines on each patch the program searches 5 8 iteratively for the patch index and U V coordinates of the point closest to the input point as explained in Section 4 6 In this case the supplementary output file gdf bpo contains the following data for each point gdfBPO K M NP U V R I XI XN Here K is the body point index M is the quadrant index NP is the patch index and U V are the parametric coordinates on the patch R is the radial distance from the point U V on the patch to the specified x y z point I is the number of iterations A maximum of 16 iterations are used in this search and if I 17 this indicates noncovergence of the search XI is the position vector of the output point on the body surface and XN is the normal vector at XI both in body coordinates 5 6 AUXILIARY FILES FOR HYDROSTATICS hst AND EXT
361. odies with generalized modes is discussed below in Section 9 5 Each generalized mode is defined by specifying the normal velocity in the form Din Nj Uh VjNy Why 9 1 where j gt 6 is the index of the mode The first six indices j 1 2 6 are reserved for the conventional rigid body modes The displacement vector uj vj w is defined by the user in a special subroutine which can be accessed and modified by the user The displacement vector can be any physically relevant real function of the body coordinates x y z which can be defined by FORTRAN code Corresponding to these modes are the generalized hydrodynamic force components which are defined as in Sections 3 2 and 3 3 with the extended normal vector n and the corresponding radiation solutions y Further discussion of the pertinent theory may be found in References 13 and 26 The following examples are intended to illustrate applications The first four are sim plified from the computational examples in 13 1 A ship with simplified transverse and vertical bending modes described by the Leg endre polynomial of order 2 U7 0 U7 P2 q W7 0 9 2 Us 0 Vg 0 Wg Po q 9 3 91 Here NEWMDS 2 P3 q sq 5 is the Legendre polynomial and q 2x L is the normalized horizontal coordinate varying from 1 to 1 over the length L of the ship 2 A vertical column bottom mounted with three orthogonal cantilever modes described by shifted Ja
362. ody in the trimmed condition This submerged surface can be plotted and visualized in the same manner as for untrimmed bodies using the parameter IPLTDAT as explained in Section 4 7 The transformation from GDF coordinates to body coordinates is defined by the fol lowing relations g EC2 NS283 CS2C3 y NC3 683 z sa C283 Ccoc3 XTRIM 1 where c cos XTRIM 2 se sin XTRIM 2 c3 cos XTRIM 3 ss sin XTRIM 3 The perspective figures in the Appendix Section A 2 are useful to illustrate this trans formation The original GDF coordinates for the body are as shown in the first figures for TEST22 with the vessel in its conventional orientation The GDF inputs for TEST22a are the same except that the draft and tank depths are increased so that after vertical trimming and applying the roll angle the entire surface is still submerged After trimming the vessel is as shown in the perspective figures for TEST22a which correspond to the new body coordinates with the z axis vertically upward The WAMIT outputs which result from TEST 22a are the same as if the original GDF data defined the configuration shown in the TEST 22a perspective figures without trimming and with the hull and tank waterlines as shown in these figures The geometric output files test22a_pat dat test22a_pan dat test22a_low gdf all correspond to the latter figures not to the original un trimmed GDF data It is recommended to plot and visualize
363. of a body which is symmetric about X 0 Depending on the number of relevant modes and symmetry planes NLHS 1 2 or 4 The minimum number of influence coefficients which must be stored is equal to the product NLHSx NEQN However additional matrices may be required depending on the input parameters ILOG and ISOR in the configuration file ILOG 0 or 1 in all cases ISOR 0 or 1 for the low order panel method and ISOR 0 for the higher order method For the real components 4 bytes are required for each coefficient and the total storage required for all matrices is S Q NEQN where Q 4x NLHS x 1 4 x ISOR x 1 ILOG 14 2 For the complex components 8 bytes are required for each coefficient and the total storage required for all matrices is Se Q NEQN where Qe 8 x NLHS x 1 4 x ISOR 14 3 These can be estimated using Figure 14 1 with the factor Q defined in 14 2 3 Note that 4 lt Q lt 160 and 8 lt Qe lt 64 In three special cases Q is greater by a relatively small amount 1 in the low order method if the scattering parameter ISCATT 1 in the configuration files 2 if pressure surface panels or patches are used as described in Section 12 5 or 3 if PER 0 is assigned in the POT file corresponding to zero wave period or infinite frequency More significantly if multiple processors are used NCPU gt 1 the factor Qc must be multiplied by NCPU See Section 14 6 14 4 DATA STORAGE IN RAM In Version 7 prov
364. of the velocity potential Further details and examples based on this method are contained in Reference 25 The domain of parameters must be 1 1 in analytic representation The formulae required to define the geometry must be coded in FORTRAN in the file GEOMXACT F This file can be compiled separately as a dll file and linked with WAMIT at runtime This special arrangement makes it possible for users of the PC executable code to modify GEOMXACT for their own particular applications Another feature of this option is the possibility to input relevant body dimensions in the GDF file Thus the body dimensions can be changed without modification of the code In the version of GEOMXACT F and GEOMXACT DLL as supplied with the WAMIT software there are several subroutines to produce various generic body shapes as listed in the table below Most of these subroutines are illustrated in the higher order test runs described in Appendix A The dimensions of these generic bodies can be modified by introducing appropriate data in the GDF file Thus there is a variety of possibilities for exploiting this option with or without special programming efforts Several different subroutines can be collected in a library and identified with specific reserved values of the index IGDEF which is input in the GDF file The WAMIT software includes the FORTRAN library file GEOMXACT F where several examples of these subroutines are included Note that IGDEF 0 1 2 are reserv
365. oid In the higher order method ILOWHI 1 the solution for the velocity potential and pressure is represented by continuous B splines on each patch For each specified input point x y z the program searches for the patch index and parametric coordinates U V of the point on this patch which is closest to the input point The pressure and velocity are evaluated at the corresponding point U V An iterative procedure is used to find U V with a specified convergence tolerance of 1 0E 4 for the radial distance in nondi mensional Cartesian coordinates When the length scale of the patch is larger than 1 0 the tolerance is increased by a factor equal to this length scale estimated from the Jaco bian of the parametric transformation at the center of the patch A warning message is generated if nonconvergence occurs for one or more input points showing the total number of unconverged points See also Section 5 5 The pressure and velocity are output in the 5p and 5vx files as explained in Section 5 5 Data related to the coordinates of the evaluation points are tabulated in the supplementary output file gdfbpo which is explained in the same Section In both the low order and higher order implementations the input data in the bpi file should correspond to points which lie as close as possible to the body surface If points in the BPI files are very close to intersections of adjacent patches in the higher order method the index NP in the
366. old rotational symmetry spars and buoys often have rotational symmetry of some order the Hibernia bottom mounted platform is a 16 pointed symmetric star Four leg TLP s also usually have 4 fold rotational symmetry but this case is best treated as combined X and Y mirror symmetry because of the large efficiencies that result from exploiting mirror symmetry during the WAMIT solution In MultiSurf when the object being modeled has complete rotational symmetry it is very beneficial to take advantage of it as only a fraction 1 N of the total structure then needs to be explicitly modeled Rotational symmetry is a model level property Z axis rotational symmetry is only allowed when X and Y mirror symmetry flags are OFF In the Settings Model dialog check X Y and Z mirror symmetry OFF Z axis rotational symmetry ON and enter the number of copies e g 3 for a 3 leg TLP Then you can model only the active or independent sector of the model e g 1 leg and 2 half pontoons of a 3 leg TLP and the copies will be present implicitly The symmetry images will be shown automatically in Render view and can be toggled on and off in Wireframe view with the lt F5 gt key In the GDF file for a body using rotational symmetry about the Z axis ISX and ISY will be 0 and NPATCH needs to include the symmetry images For example if a 3 leg TLP is C 8 modeled with 11 wetted surfaces in the explicitly modeled 120 degree sector NPATCH wi
367. on or lifting effects The free surface and body boundary conditions are linearized A harmonic time dependence is adopted The Cartesian coordinate system x y z is defined as shown in Figure 4 1 fixed relative to the undisturbed positions of the free surface and body with the z axis positive upwards The body geometry input to WAMIT is defined relative to the body coordinate system and the incident wave system is defined relative to the global coordinates as explained in Chapter 3 and Section 4 2 For the sake of simplicity here it is assumed that these two coordinate systems coincide The assumption of a potential flow permits the definition of the flow velocity as the gradient of the velocity potential satisfying the Laplace equation Vo 0 15 1 in the fluid domain The harmonic time dependence allows the definition of a complex velocity potential y related to by Re ye 15 2 where Re denotes the real part w is the frequency of the incident wave and t is time The ensuing boundary value problem will be expressed in terms of the complex velocity potential p with the understanding that the product of all complex quantities with the factor e applies The linearized form of the free surface condition is y Kp 0 on 2 0 15 3 Here K w g is the infinite depth wavenumber and g is the acceleration of gravity The velocity potential of the incident wave is defined by igA cosh k z H erika cos 8 ik
368. ons include the total length XL transverse coordinates of the inner outer pontoon sides Y1 Y2 and vertical coordinates of the bottom and top horizontal surfaces Z1 Z2 Note that 0 lt Y1 lt Y2 and Z1 lt Z2 lt 0 The overall beam is equal to 2x Y2 and the draft is equal to Z1 The pontoon ends are semi circular NPATCH depends on the number of columns and their spacing as explained in the subroutine header If Z2 0 and NPATCH 2 the pontoons intersect the free surface The test run TEST15 illustrates the use of this subroutine for a semi sub with submerged pontoons and five columns on each pontoon FPSO defines a monohull ship with a form representative of the Floating Production Ship Offloading type A perspective view of this vessel is shown on the cover page The hull consists of three portions 1 an elliptical bow with a flat horizontal bottom vertical sides and semi elliptical waterlines 2 a rectangular mid body with a flat horizontal bottom vertical sides and constant beam and 3 a prismatic stern with rectangular sections The dimensions XBOW XMID XAFT define the longitudinal extent of these three portions The total length of the vessel is equal to XBOW XMID XAFT and the origin of the coordinate system is defined at the midship section half way between the bow and stern The dimensions include the half beam HBEAM half width of the transom HTRANSOM maximum draft DRAFT and transom draft DTRANSOM In the general case
369. or if necessary in cases where NEQN is very large the block iterative solver ISOLVE gt 1 Results from convergence tests using the low order method have been published in Ref erences 5 6 9 10 and 12 The accuracy of the evaluated quantities has been found to increase with increasing numbers of panels thus ensuring the convergence of the discretiza tion scheme The condition number of the linear systems is relatively insensitive to the order of the linear systems and sufficiently small to permit the use of single precision arithmetic Convergence tests for the higher order method are reported in References 18 19 20 24 and 25 14 3 TEMPORARY DATA STORAGE From the computational standpoint the principal tasks are to set up and solve the linear systems of equations for the unknown potentials and source strengths These tasks require substantial temporary storage for most practical applications either in RAM random access memory or in scratch files on the hard disk Generally access to RAM is much faster than to the hard disk but the size of RAM is relatively small The first versions of WAMIT were developed when RAM was quite small typically measured in Kilobytes and it was essential to use scratch files whenever possible WAMIT Version 7 has been developed to take advantage of the much larger RAM available in contemporary systems measured in Gigabytes 1 GB is equal to 10 bytes or 10 Kilobytes For most applications the domin
370. orce coefficients of body 1 are denoted by X j 1 2 9 the six conventional coefficients of body 2 by j 10 11 15 and the eight coefficients of body 3 by j 16 17 23 gdf GDF CONFIG WAM FNAMES WAM NEWMDS gt 0 edf GDF pot POT fre FRC DEFMOD POTEN in Figure 9 1 Flow chart showing the use of WAMIT and DEFMOD to define and analyze generalized modes in the low order method ILOWHI 0 The number of generalized modes NEWMDS is specified in the configuration file On the first run of WAMIT the centroid coordinates area normal vector n and cross product xxn are output for each panel to the file gdf PRE for pre processing by the program DEFMOD After modification by the user to specify the desired modes DEFMOD is run with the input file gdf PRE to produce the output file gd MOD containing the normal velocity of each new mode at the panel centroids and also the hydrostatic coefficients After this pre processing is completed WAMIT is run again in the normal manner as in the flow chart of Figure 1 1 Note that WAMIT reads the GDF and POT input files on both runs although the data in the POT file is only used on the second run Chapter 10 USE OF IRREGULAR FREQUENCY OPTION WAMIT includes a method for removing the effects of irregular frequencies on both the velocity potential and the source strength An outline of the method is given in Section 15 7 with more d
371. order to provide examples for relatively large computations the input parameters for these two runs have been modified as explained in the caption Users should first verify the number of CPU s and size of RAM of the system For Windows systems the RAM size is displayed after selecting Start Control Panel Sys tem The number of processors is listed under Advanced Environment Variables NCPU should be determined based on the number of physical processors also referred to as cores and not based on the number of hyper threads If the system includes more than one CPU open the file config wam with a text editor The default settings in this file are as follows NCPU 1 RAMGBMAX 0 5 Change NCPU to the appropriate number for the system and increase RAMGBMAX to the maximum value which can be used for scratch memory following the guidelines in Section 14 4 Note that the RAM required for multiple processing is proportional to 14 8 NCPU The actual RAM required during a run is displayed in the output file wamitlog txt If RAMGBMAX is not sufficiently large for the value of NCPU specified the program stops with an error message displayed In that case the user should reduce NCPU or modify the other input parameters to increase RAMGBMAX or reduce the required RAM 30 25 20 s TESTO7m 15 S TEST15m 10 TIME min q 3 NCPU Figure 14 2 Run times
372. ould be set equal to one 4 3 THE FORCE CONTROL FILE Alternative form 1 The FRC file is used to input various parameters to the FORCE subprogram The name of the FRC file can be any legal filename accepted by the operating system with a maximum length of 16 ASCII characters followed by the extension frc In this Section the first form of the FRC file is described in which the input of the body inertia matrix is simplified and it is assumed that the body is freely floating The data in the Alternative 1 FRC file is listed below header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 VCG XPRDCT 1 1 XPRDCT 1 2 XPRDCT 1 3 XPRDCT 2 1 XPRDCT 2 2 XPRDCT 2 3 XPRDCT 3 1 XPRDCT 3 2 XPRDCT 3 3 NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XFIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XFIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD The definition of each variable in the Force Control File is as follows header denotes a one line ASCII header dimensioned CHARACTERx72 This line is available for the user to insert a brief description of the file with a maximum length of 72 characters including leading blanks IOPTN is an array of Option Indices These indicate which hydrodynamic parameters are to be evaluated and output from the program The available options descriptions and filenames of the numeric output files are
373. ource file newmodes f for further information For bodies with submerged FSP surfaces the volumes and center of buoyancy are com puted in the same manner as if these surfaces were part of the body Thus the displaced 12 15 volume includes the volume between the submerged FSP surface and the exterior free sur face which ensures that the body is in hydrostatic equilibrium if the hydrostatic force on the FSP surface is balanced by an equal and opposite force on the body The hydrostatic restoring coefficients C are computed separately on the wetted surface Sw and the pressure surface Sp these surfaces are defined in Section 15 11 For the six rigid body modes the equations in Section 3 1 are used with S replaced by Sw For the additional pressure modes the restoring coefficients are defined by equation 15 77 The volumes VOLX VOLY VOLZ and center of buoyancy are evaluated using the equations in Section 3 1 and integrating over the entire surface Sp Sw Sp There is no contribution from the pressure surface S if this is in the same plane as the exterior free surface Z 0 but if S is submerged below Z 0 there are nonzero contributions which affect the volumes and center of buoyancy as in TEST25 If the body is freely floating and IALTFRC 1 is used see Section 4 3 this implies that the mass and horizontal components of the center of gravity are the same as for a conventional body with the same total volume Depending on the
374. panel offsets and to all related parameters in the other input files The coordinate system x y z in which the panels are defined is referred to as the body coordinate system The only restrictions on the body coordinate system are that it is a right handed Cartesian system and that the z axis is vertical and positive upward The name of the GDF file can be any legal filename accepted by the operating system with a maximum length of 16 ASCII characters followed by the extension gdf The data in the GDF file can be input in the following form header ULEN GRAV ISX ISY NPAN X1 1 Y1 1 Z1 1 X2 1 Y2 1 Z2 1 X3 1 Y3 1 Z3 1 X4 1 Y4 1 Z4 1 6 2 Figure 6 1 Discretization of a circular cylinder showing the convention for panel vertex numbering The perspective view is from above the free surface showing portions of the exterior and interior of the cylinder lower and upper portions of the figure respectively The view of panel is from the wet side inside the fluid domain so the vertex ordering appears anti clockwise The view of panel j is from the dry side outside the fluid domain so the vertex ordering appears clockwise X1 2 Y1 2 Z1 2 20 Y2 2 200 X3 2 7302 Z3 2 X4 2 Y4 2 Z4 2 X4 NPAN Y4 NPAN Z4 NPAN Each line of data indicated above is input by a separate FORTRAN READ statement hence line breaks between data must exist as shown Additional line breaks between data shown above ha
375. period IFREQ 1 infinite or zero period When IFREQ 1 the total and diffraction pressure coefficient are not output in 5pb WRAO I J Complex motion amplitude I modes J wave heading WPRS Total pressure coefficient I unknown coefficient M reflection J wave heading WBD Diffraction pressure coefficient I unknown coefficient M reflection J wave heading MDI Mode index WBR Radiation pressure coefficient I unknown coefficient ICOL MDI pointer of mode MDI 5 5 BODY PRESSURE AND VELOCITY AT SPECIFIED POINTS As explained in Section 4 6 the body pressure and velocity can be evaluated at specified points on the body using the special input file gdf bpi to input the coordinates of these points In this case the pressure is output in the 5p numeric output file with the following format OPTN 5P PER BETA IBODY IPOINT Mod p Pha p Re p Im p This format and the definitions of the data are the same as in Section 5 2 except that the index IBODY is used to specify the body index and IPOINT is used to specify the index of the input point in the bpi file J 1 2 NBPT for each body Similar output files 5vx Svy 5vz contain the components of the fluid velocity on the body surface in the same format when IOPTN 5 gt 2 In addition to these hydrodynamic outputs a supplementary file gdf bpo Body Point Output is output to provide information about the actual points where these evaluations are made If the low order meth
376. pg ynadS pyVr2c T Cr 4 5 pg I ryn3ds Sr Cr 4 6 pgYr Te Cr 5 5 pg I r nadS pgYTZe T Cr 5 6 pgYrye All other elements of the matrix Cr are equal to zero Here Yr VOLTANK 1 i ndS Sr Vr VOLTANK 2 I ynodS Sr Yr VOLTANK 3 I z Zr nads Sr 1 2 Te wil he nids a hees Ye 2Vr ST y ig 1 2 2 To Z2 ngds z N he 7 n3dS In WAMIT the hydrostatic parameters of the hull and tanks are evaluated separately Thus VOL C i j are evaluated for the hull ignoring tank patches panels and their values are the same with or without tanks as defined in Section 3 1 The corresponding tank 15 16 parameters VOLTNK 1 3 1 NTANK and CTANK 1 9 1 NTANK are evaluated separately for each tank the second index is omitted for simplicity of notation CTANK 1 _ nad CTANK 2 ends CTANK 3 A vnads CTANK 4 2m d5 CTANK 5 i Pnad CTANK 6 Zonas CTANK 7 Pnad CTANK 8 i A curas CTANK 9 I and It is necessary to consider the implications of planes of symmetry with respect to the tanks If all of the tanks are symmetric about a plane of symmetry then it is appropriate to use that option assuming the hull is also symmetric about the same plane Thus for example for a hull with symmetry about y 0 and with all tanks symmetric about the same plane it is appropriate to set IS 2 1 But if there are two or more t
377. plane area As the process continues moving inward toward the centroid the panel size can be increased and the continuity between adjacent panels is less important 10 2 AUTOMATIC FREE SURFACE DISCRETIZATION IRR 2 and ILOWHI 0 If IRR 2 is input in the low order method ILOWHI 0 the program projects the body panels onto the free surface to generate panels on the free surface The GDF file contains only the body panels it is the same as the GDF file used with IRR 0 IRR 2 should not be specified for a body such as a Tension Leg Platform or semi sub with pontoons or more generally for any body where a vertical line intersects the body surface more than once and thus the projection of two body panels overlap on the free surface A warning message is issued for any panel where the inward normal vector slopes downward away from the free surface unless the panel is entirely in the plane of the free surface Panels which are entirely in the plane of the free surface are ignored Dipole panels are ignored This simple procedure is effective for bodies such as the circular cylinder used in Test01 consisting of flat horizontal panels on the bottom which are projected up to the interior free surface and vertical panels on the sides which are ignored in defining the interior free surface Since dipole panels are ignored this procedure can be applied for the spar with helical strakes used in Test09 10 3 AUTOMATIC FREE SURFACE DISCRETIZATION
378. ppendix C Using the WAMIT RG Kernel Interface J S Letcher Jr AeroH ydro Inc Southwest H arbor M aine 04679 USA 207 244 4100 Sept 8 2002 revised June 21 2006 revised Sept 20 2008 revised Oct 20 2011 Contents Using the WAMIT RGKernel Interface ccccsssesssetesssseseseessesesesansseeseseseeeceseseserseseeneaeaeas 1 CONTENTS a Re nee Par ee Pree oer rma O SA a A Ra a ae A a ner 1 Tintrod cdiomn a se sr sats ace ch a aaa 1 1 1 New features for WAMIT version 6 4 c cccsceesseeseesceeseesecesecesecaecaeceneeeneeeeeeeeeeeeseeeseceaeeeaeenaeeneeates 2 2 Supported features and OPW ONS i viscatscaiscie asessncsestcrcccenteree snsstel cvasknenetdesessensuenavsteris iantoeincredas 3 3 Required files versions and file lOCati ONS eseeeeeeeeeeseeeeeeeeseeeeeeeeeeeeeseseetsneeseeeeeeeneeees 4 4 MultiSurf modeling considerations rrenan nana 4 4 1 Trimmed surfaces are excluded ccccesccesecsseesseeseesseeeeceeeesecsecaeceecesecaecsaecaeecaeeeaeseneseneeeneeeaeenee 4 4 2 Optional wetted surface Entity List ec eeessesecsesseceseeeceseceeesecseesecnassecsaeeeesaecaeesesnerseesaeeneeaeeaee 5 4 3 Order OF patches ss iernare aaea ea aa E S E ERNA 6 4 4 Surface normal orientations ceccesecesecececceeseeeneeeceesecesecesecsseceaeceaecaeecaeecaeseseeeeeeeseeereeeeneenseenee 6 4 5 Baseplaj and waterline ii l err e eaan foda fed nao apto aaa E aA E E E SK N EAREN 7 4 6 Mitroi sy MMEY sonare a s na
379. pproximation can be systematically refined by increasing the number of panels or by using the PANEL SIZE option in the CONFIG WAM or CFG file and reducing the value of this parameter In TEST 11a the geometry is defined analytically by the GEOMXACT F subroutine CIRCCYL IGDEF 1 The radius and draft of the cylinder are input in TEST11a GDF The parameter INONUMAP 0 specifies uniform mapping Comparison of the output files with TESTO1 and TEST11 confirms the statements above regarding accuracy Most of the output data from TEST11 and TEST 11a agree to at least five decimals except for the third wave period which coincides with an irregular frequency In TEST11b the geometry is defined analytically in the same manner as for TEST 11a except that nonuniform mapping is specified by the parameter INONUMAP 1 as explained in Section 6 8 This modification gives a more accurate solution near the corner and wa terline which is particularly beneficial for the pressure drift force evaluation Comparison between the outputs for the momentum and pressure drift force shows that the results are more consistent in this case compared to the use of uniform mapping in TEST11a More extensive comparisons for the same geometry are included in Reference 24 TEST 11c illustrates the use of the option IGDEF 2 where the geometry is described by MultiSurf see Section 6 7 and Appendix 2 In this case the same nonuniform mapping is used as in TEST11b using the relab
380. pressure distributions acting on the FSP surfaces are defined in a manner similar to the representation of generalized modes using subroutines in the file newmodes d11 as described in Chapter 9 In the simplest case the pressure distribution is constant and only one mode is required for each FSP surface In more general cases the pressure distribution can be represented by appropriate sets of modes such as Fourier modes The parameters IMODESFSP and NMODESFSP specify for each body the sub routine used to define the modes and the number of active modes respectively These are analogous to the parameters IGENMDS and NEWMDS used for generalized modes Each pressure mode is assigned a mode index j gt 6 and a complex amplitude In the case of one body or body one if there are multiple bodies the pressure distribution is defined by the equation 6 Mp polz y pg 5 Emig y j 7 where M NMODESFSP is the number of pressure modes and the spatial distribution of each mode is described by the real function n x y The standard distribution version of newmodes d11 includes the subroutine PRESSURE FS which permits the representation of a constant pressure distribution on a surface Symmetric and antisymmetric modes can be used to analyze cases such as that described in Appendix A25 with appropriate planes of symmetry and with independent pressures acting on separate surfaces Users should refer to the comments in this subroutine in the s
381. put file testi5 spl TEST15 Semi sub NCOL 5 IGDEF 10 9 2 NU NV patch 10 32 pontoon bottom 32 1 NU NV patch 9 32 pontoon side 2 2 NU NV patch 1 32 column 3 24 NU NV patch 2 32 annulus 3 5 2 NU NV patch 3 32 between annulus 3 amp 4 4 2 NU NV patch 4 32 column 4 4 1 NU NV patch 5 32 annulus 4 5 2 NU NV patch 6 32 between annulus 4 amp 5 4 2 NU NV patch 7 32 column 5 4 1 NU NV patch 8 32 annulus 5 Input file testi5 frc TEST15 Semi sub with five columns on each pontoon 1 1 1 1 0 0 14 1 1 0 0000 20 0 0 0 0 0 0 60 0 0 0 0 O 60 0 0 0 Input file testi5 csf testib csf semi sub outer box 150 60 40 1 ILOWHICSF 1 1 ISX ISY O O 10 NPATCH ICDEF PSZCSF 1st two indicate this is automatic 0 0 40 0 RADIUS DRAFT of outer box 4 NPART 3 nvo 150 0 0 0 150 0 60 0 0 0 60 0 3 nvi end of partition line O outer boundary of control surface 0 30 0 30 0 4 nv2 30 30 90 90 3 nv3 90 0 50 0 90 0 0 0 150 0 0 0 end of partition line column 3 A 16 BARGE WITH BENDING MODES TEST16 The test runs TEST16 and TEST 16a analyze the structural response of a rectangular barge with total length 80m beam 10m and draft 5m Eight free free beam modes are included to analyze the elastic deformation of the barge These mode shapes are defined in the NEWMODES subroutine FREEBEAM_X and the length is input to this subroutine using the file test16_Length dat as described in Section 9 3 The
382. quency infinite wave period which is identified in the output files by a negative value of the parameter PER and also in the case of infinite frequency zero wave period which is identified by PER 0 In general for nonzero finite values of the frequency the nondimensional outputs for the radiation pressure and velocity are as defined in Sections 3 5 and 3 7 Thus the output pressure for each radiation mode is KLy and the output velocity for each mode is KLV However for the two limiting cases where KL 0 or KL the factor KL is omitted from the outputs for Options 5 and 6 The following table summarizes these definitions frequency period pressure velocity PER lt 0 w 0 OO Pj VQ 0 lt PER lt co 0 lt w lt oo 27 w KLp KLV PER 0 W 00 0 Pj VQ Chapter 4 INPUT FILES A typical application of the WAMIT program will consist of a preparing appropriate input files b running WAMIT and c using the resulting output files Most of the required input files are generic with the same format and data irrespective of whether the low order or high order method is used These files are described in this Chapter The principal exception is the geometric data file GDF which is described separately for the two methods in Chapters 6 and 7 respectively To simplify the presentation this Chapter will describe the required input files for a basic application involving the analysis of a single body Further information is given
383. r Options 5 and 6 which may be useful for special purposes A distinction is made between radiation and diffraction components Radiation components are output from WAMIT separately if INUMOPT5 1 and or INUMOPT6 1 and IRAD 0 or 1 All other outputs are of the diffraction type including both the separate diffraction components of the pressure and velocity and the total superpositions which are output when INUMOPT5 0 and or INUMOPT6 0 The diffraction type pressure and velocity are transformed in the same manner as the exciting forces and RAO s The IRFs K t are evaluated using 13 10 with X the frequency domain output from WAMIT for the same pressure or velocity The free surface elevation is equivalent to the pressure on z 0 as defined in Section 3 6 The radiation components of the pressure are not output directly by F2T Instead the radiation potentials defined in Section 3 5 are transformed using 13 5 6 with the real and imaginary parts of the potential substituted for the added mass and damping The radiation components of the fluid velocity are defined as the nondimensional gradients of these potentials as in Section 3 7 If IDIFF 1 is specified in the WAMIT run the WAMIT outputs from Options 5 and 6 are the total responses from superposition of all specified radiation modes If more than one mode is considered the output is for nonzero finite frequencies only and is not suitable for transform to the time domain un
384. r WAMIT should choose this option The MultiSurf for WAMIT Users option is the same as the typical version but for users that will be installing MultiSurf for WAMIT Both the typical and MultiSurf for WAMIT install options permit the modification of the install directory as shown in Figure 2 3 The recommended name is c wamitv7 but the user may prefer to use a different drive or directory name with a maximum length of 40 characters for the string This directory should be accessible by all users on the computer If a different drive or directory name is used this must be specified as USERID_PATH in the configuration file as explained in Section 4 7 Users that are upgrading WAMIT either with or without MultiSurf for WAM IT can choose either of these options providing they have not modified their existing geomxact f newmodes f and the associated DLLs Users that are upgrading WAMIT and have modified existing geomxact f newmodes f and the associated DLLs should select the Custom installation button or make a backup 2 2 of these files before using the typical or MultiSurf for WAMIT option The custom op tion panel is shown in Figure 2 4 To deselect the installation of the geomxact f and newmodes f source and DLL files select Supplemental Dlls and choose Entire feature will be unavailable If you are a MultiSurf for WAMIT user also select MultiSurf Com ponents and choose the same thing To modify the installation
385. r a substantial time This may be inconvenient for the user especially if it is desired to check a few outputs for the initial wave periods prior to the completion of the run Also if the run is interrupted prior to completion all of the computed data is lost unless the special procedure described in Section 4 12 is used If IFORCE 2 and NCPU 1 the computations of POTEN and FORCE are executed in sequence for each wave period and the outputs from the intermediate numeric output files of FORCE are available as soon as each wave period is completed The optn filename is used for these intermediate outputs in POTEN After completion of the POTEN period loop the same data are written to the numeric output files with the filenames frc or optn depending on the configuration parameter NUMNAM and to the file frc out The optn files will be overwritten in the next WAMIT run without warning During a long POTEN run the data which has been evaluated in the optn files can be read with a text editor but should not be re saved with the same names to avoid conflicts during the 4 47 WAMIT run When multiple processors are used NCPU gt 1 with IFORCE 2 POTEN and FORCE are executed in the same manner as described above However the data in the optn files are not output until after the period loop is completed and thus it is not possible to access these outputs during the execution of POTEN Chapter 5 OUTPUT FILES Several output files
386. r example the input POT file for the first test run listed below is TEST01 POT The first character of tst is O for low order test runs ILOWHI 0 and gt 1 for higher order test runs ILOWHI 1 Test runs which are identical except for different input options are assigned the same number with a letter suffix For example TEST11 and TEST11la c describe the same physical problem using different options to represent the geometry B splines exact analytic formulae MultiSurf uniform and nonuniform mapping In TEST14 the ISSC TLP is analysed and the use of the fixed mode option is illustrated In TEST14a the same geometry is analysed for a large number of input frequencies including zero and infinite frequencies and the outputs are postprocessed by the F2T utility In TEST16 a rectangular barge is defined by the subroutine BARGE IGDEF 5 and in TEST 16a the patches are defined by flat panels IGDEF 0 Tests 17 and 17a c illustrate alternative methods for analyzing a body with moonpools as explained in Section A 17 Tests Ola 09a 13a and 22a are examples showing the use of trimmed waterlines ITRIMWL 1 tst 01 Ola 02 03 04 05 05a 06 07 08 09 09a 11 lla 11b llc 12 13 13a 14 14a 15 16 16a 17 17a 17b 17c 18 19 20 21 22 22a 22b 23 24 25 description Circular cylinder Circular cylinder Circular cylinder Circular cylinder Barge near wall Cylinder amp spheroid Cylinder amp spheroid ISSC TLP coarse IS
387. r is prompted at the start of the FORCE subprogram with the choice of either overwriting the old file test01 out or specifying another name for the new OUT file If the default setting NUMNAM 0 is used the same safeguard will apply to the numeric output files minimizing the possibility that these are lost during a subsequent run Otherwise if NUMNAM 1 the OPTN output files are assigned the same names for all runs and old OPTN files are overwritten without warning when a new run is made this option avoids the proliferation of old output files but requires the user to rename or otherwise preserve the contents of OPTN files which are to be saved For batch processing it is important to avoid interactive interrogation from the programs Thus the user should delete or rename P2F and or OUT files from previous runs if the same names will be assigned from the POT and or FRC control filenames respectively in a new run Starting in Version 7 1 the configuration parameters IDELFILES IOUTFNAME and IOUTLOG can be used to control and modify filenames automatically as explained in Section 4 7 There are four options IDELFILES 1 4 to delete and overwrite the P2F and OUT files If the parameter IOUTFNAME is used with the value N 1 4 the OUT output file is given a unique filename ending in M where the integer M is assigned in ascending order using N digits If the default setting NUMNAM 0 is used all of the output files from the run are given the
388. r the subroutine NEWMODES to define generalized modes as described in Chapter 9 The following points are intended to provide further background information and should be consulted in conjunction with the code and comments in GEOMXACT e The principal inputs are the parametric coordinates u v represented in the code by scalars U and V e The principal outputs are the Cartesian coordinates X represented by the array X of dimension 3 and the corresponding derivatives with respect to U V which are represented by the arrays XU XV with the same dimension e These arguments and all associated dimensions are of type REAL 4 single preci sion e Ina typical run GEOMXACT is called a very large number of times Users modifying this code should ensure that the new code is efficient from the standpoint of CPU time e The arrays X XU XV are initialized to zero before calls to GEOMXACT Thus it is only necessary to evaluate nonzero elements in the subroutine e Other inputs in the argument list include the body index IBI to distinguish multiple bodies the patch index IPI and the parameter IGDEF all of type INTEGER The symmetry indices ISX ISY irregular frequency parameter IRR and NPATCH have been added to the argument list of GEOMXACT to permit use of these inputs in special cases e To facilitate reading user specified data in the GDF file an initial call is made to GEOMXACT with IPI 0 to designate this purpose If the user inte
389. raction solutions The same line is reproduced in the header of the OUT file This display during the run permits the user to monitor the progress and estimate the total time to complete the run The optional input file break wam can be used to activate break points during the POTEN run This makes it possible to break a run when the computational time is excessive without losing data that has already been computed The use of break wam is optional and if break wam does not exist in the default directory the run will continue normally without any breaks It is possible as described below to input break wam after the WAMIT run has started in order to break a run which is taking more time than was expected at the start of the run If the input file break wam exists and can be opened without an error the user is prompted at two break points within the loop over NPER wave periods The first break point is at the beginning of the period loop before setting up the linear system and the second break point is after setup is completed but before solving the linear system Since the relative balance of time required for setup and solution depends on the inputs two opportunities to break the run are provided When a break occurs the monitor displays a message to identify the break point fol lowed by a menu of options The two messages for the first and second break points are as follows gt Break at start of period loop period JPER
390. re obvious but in some cases extra com putation would be required and the program is intended to perform this computation automatically However in some cases the program may not identify end points which should be moved to the outer boundary and the user should verify that this has been done correctly by plotting the data in the auxiliary file gdf csf dat This problem can be avoided by specifying the correct vertex coordinates in the CSF file for the outer ends of the partitions Automatic definition of the intermediate free surface may fail in some cases where the waterlines are irregular Examples of irregular waterlines where the automatic option may fail include 1 locally concave waterlines 2 moonpools 3 bodies with thin elements dipole patches which intersect the free surface e g TEST21 and 4 bodies with horizontal patches or panels in the plane of the free surface It is advisable to confirm the representation of automatic control surfaces by plotting the data in the auxiliary file gdf_csf dat In cases where only the horizontal components of the drift force and vertical component of the drift moment are required the intermediate free surface can be omitted The option to use two separate CSF files described in Section 11 4 above should not be used for automatic control surfaces When automatic representation of the control surface is used special values must be assigned to the parameters NPATCSF and ICDEF a
391. recting erroneous inputs Output files containing warning and error messages are created after each execution of the subprograms POTEN and FORCE errorp log contains messages from POTEN and errorf log from FORCE These files are overwritten with every new run When the program runs success fully without any warning or error the LOG file contains two lines a header line including the date and time when the program starts to run and a line indicating the completion of the run Error messages are associated with problems where the program execution is halted Warning messages indicate that a possible error may occur but under certain circumstances the results may be correct Examples include failure of the convergence tests for various numerical integrations which sometimes result from inappropriate choices of characteristic length scales or of overly conservative convergence tolerances Another example is in the case of diffraction by a body with one or two planes of symmetry where it is possible to compute the fluid pressures velocities and mean drift forces Options 5 9 at certain heading angles without solving for all components of the diffraction potential in this case the warning message states that the solution is non physical whereas at some heading angles the outputs will be correctly evaluated For further discussion of this shortcut see the discussion of MODE in Section 4 2 and related discussion in Section 4 3 The same messag
392. red However the use of generalized modes is more general and also has the advantage that the desired structural loads and total forces can both be evaluated during the same FORCE run The use of NPFORCE or NPNOFORCE only affects the integration of the hydrodynamic pressure on the body surface and the outputs for FORCE options 1 added mass and damping coefficients and 3 exciting forces from diffraction potential It does not affect the hydrostatic restoring coefficients defined in Section 3 1 Results for the RAO s and other outputs which depend on the body motions will usually be incomplete or non physical 12 17 Chapter 13 THE F2T UTILITY The Fortran utility F2T Frequency to Time domain is a post processor to transform frequency domain WAMIT output to time domain impulse response functions IRFs This program is intended to provide a utility which can be used for general purposes based on standard WAMIT outputs This program accepts as input all of the first order linear outputs from WAMIT including any combinations of Options 1 6 added mass damping Haskind exciting forces Diffraction exciting forces RAO s body pressures velocities field point pressures velocities In principle there are no restrictions regarding the numbers of rigid body modes generalized modes or bodies The computed IRFs are saved in output files which are analogous to the input files for each option and use the same filename extensions Th
393. ree surfaces remain level when the vessel is trimmed Further information is given in Section 12 2 This option is illustrated in TEST22a where the vessel is given a heel static roll angle of 15 degrees and also in TEST22b where the tanks are partially filled When this option is used the geometry of the internal tank surfaces must be defined up to or above the trimmed free surface of the tank Special attention is necessary if the origin of the body coordinate system is above or below the plane Z 0 of the exterior free surface XBODY 3 K is nonzero in the Potential Control File as defined in Section 4 2 If ITRIMWL 0 or if ZTANKFS is not included in the CFG file and ZTANKFS is assigned by the program from highest point of the panel vertices or patch corners defining that tank the value is assigned in body coordinates However if ZTANKFS is assigned in the CFG file it must be defined there in global coordinates to correspond with the elevation above the exterior free surface In all cases when tanks are included the values of ZTANKFS shown in the Tank parameters list in the header of the out file are defined in body coordinates to be consistent with the hydrostatic parameters of the tanks These details are illustrated in TEST22b The solutions for the velocity potential or source strength are performed independently for the exterior fluid domain and for each interior tank Thus the mutual locations of these surfaces are irrelevant
394. ree lines are copied from the GDF in put file The total number of sub divided panels is included on line 4 This option can be used to increase the number of panels and hence to increase the accuracy of the solution for the potential or source strength However this subdivision scheme does not increase the accuracy of the geometric representation of the body since the subdivided panels are coplanar with the original panels Only one body can be subdivided in this manner In the higher order method ILOWHI 1 the optional output files gdf_pat dat and gdf pan dat specify the vertex coordinates of both the patches and panels as defined in Chapter 7 These files are in the Tecplot ordered list format POINT The integer parameter IPLTDAT in the configuration files is used to specify whether or not to generate these output files In the default case IPLTDAT 0 no files are generated If IPLTDAT gt 0 the number of panel subdivisions on each patch is determined by the parameters NU and NV in the SPL file as explained in Section 7 11 If IPLTDAT 1 the data file gdf_pat dat contains only the four vertices of each patch and the file gdf_pan dat contains only the four vertices of each panel If IPLTDAT gt 1 each element is subdivided into IPLTDATxIPLTDAT sub elements Subdivision of the elements is useful when perspective plots are constructed for bodies with curved boundaries of the patches and panels When the curvature is large IPLTDAT should be increas
395. rees of freedom Now suppose that the body is restrained in the vertical modes heave roll pitch as would be the case for the first order motions of a tension leg platform This condition can be analyzed in FORCE by modifying the Force Control File in the following manner 1 assign a negative value to IOPTN 4 1 to use the Haskind exciting force or 2 to use the diffraction exciting force 2 insert two new lines of data after IOPTN before VCG or RHO NDFR MODE 1 MODE 2 MODE 3 MODE NDFR Here NDFR is the total number of possible radiation modes and MODE is an array with the value of each element 0 if the mode is fixed or 1 if the mode is free For the example described above NDFR 6 and MODE 1 1 0 0 0 1 Thus surge sway and yaw are free while heave roll and pitch are fixed When this option is employed the RAO s output for the free modes are defined in the conventional manner as the amplitudes of body motions in the corresponding degrees of freedom For the fixed modes the RAO s are replaced by the loads acting on the body in the corresponding directions In this case the corresponding modal index in the output file is shown with a negative value to signify the change For the example described above the output RAO for heave is equal to the vertical load acting on the body equal and opposite to the load on the restraining structure and preceded by the index 3 The TLP Test Runs 06 07 14 described in the
396. reflections about two planes of symmetry are required NEQN is increased by a factor of four and NLHS is reduced by a factor of one quarter Flow symmetries and anti symmetries are enforced in the solution of the integral equa tions by the method of images The collocation point x in the argument of the wave source potential is reflected about the geometry symmetry planes with a factor of 1 or 1 for symmetric and antisymmetric flow respectively Since the issue of hydrodynamic symmetry is so important it should be emphasized that the separate analysis of symmetric and antisymmetric modes of motion applies not only to the obvious cases of radiation modes such as surge sway and heave but also to the more complex solution of the diffraction problem even in oblique waves This is achieved in WAMIT by decomposing the complete diffraction or scattering solution as the sum of four separate components that are respectively even or odd functions of the horizontal coordinates Physically these can be interpreted as the solutions of problems where standing waves are incident upon the body To avoid unnecessary computations the architecture of WAMIT permits the analysis of any desired sub set of the rigid body modes and of the corresponding diffraction com ponents based on the settings of the MODE I indices in the potential control file see Section 4 2 For example if only the heave mode is specified in conjunction with the solution of the
397. resent the entire forward half of one barge as shown in the patch figure The subroutine BARGE IGDEF 5 is not suitable since this only represents one quadrant of one barge On the other hand BARGE can be used in the alternative NBODY 2 approach Input file test19 cfg TEST19 CFG Catamaran barge ipltdat 5 ILOWHI 1 IALTFRC 1 ISOLVE 1 IQUADI 5 IQUADO 4 MONITR 0 NUMHDR 1 Input file testi9 pot TEST19 POT Catamaran barge same geometry as TESTO4 HBOT SH OD WwW N oo 1 test19 gdf 0 0 0 0 1 O 1 O 1 First 10 lines of input file IRAD IDIFF NBODY test19 gdf TEST19 one quadrant of catamaran barge configuration 40 9 80665 ULEN GRAV 1 1 ISX ISY 4 0 NPATCH IGDEF 40 0000 2 000000 40 0000 22 00000 40 0000 22 00000 40 0000 2 000000 40 0000 22 00000 0 000000 22 00000 10 00000 10 00000 0 000000 0 000000 end 10 00000 10 00000 Input file testi9 spl TEST19 catamaran barge 2 2 NU NV end 4 4 KU KV 5 2 outside 4 4 5 2 bottom 4 4 5 2 inside 4 4 IQUO IQVO are not specified IQUADO 3 in config wam IQUI IQVI are not specified IQUADI 4 in config wam Input file test19 frc TEST19 FRC Catamaran barge ILOWHI 1 same as TESTO4 FRC 1 1 1 1 1 0 0 1 1 3 0 20 00000 0 000000 0 000000 0 000000 5 000000 0 000000 0 000000 0 000000 20 00000 0 0 A 20 MULTISURF BARGE TEST20 This example illustrates the use of a MultiSurf geometry representation with
398. rge number of panels in the low order method or corresponding number of unknowns in the higher order method to represent both the geometry and the hydrody namic solution with a satisfactory degree of accuracy In such cases the required storage for temporary data and the time required to set up and solve the linear systems of equations are both large From the computational standpoint the principal task is to set up and solve the linear systems of equations which correspond to the discretized integral equations described in Sections 15 3 and 15 5 The dimension of these linear systems is denoted by NEQN number of equations In the low order method NEQN is the same as the number of panels In the higher order method NEQN depends on the number of patches panels and on the order of the basis functions as explained in Section 14 1 WAMIT includes three optional methods for solving the linear systems of equations including a direct solver which is robust but time consuming for large values of NEQN an iterative solver which for large systems of equations is much faster and a block iterative solver which combines the advantages of each to some extent These methods are described and compared in Section 14 2 Section 14 3 describes the required storage for the influence coefficients on the left hand sides of the linear systems of equations These must be stored either in random access memory RAM or in scratch files on the hard disk Since access
399. run POTEN and the same TEST17a P2F file is used for TEST17b Thus TEST17a pot is specified in FNAMES 17b and IPOTEN 0 in the TEST17b cfg file The only nonzero elements of the external damping matrix are for heave j 3 and the lid vertical motion j 7 With these empirical damping coefficients added more appropriate RAO s are obtained as shown in the Figure This general approach can be refined based on experimental data Experience with similar problems suggests that relatively crude estimates based on the observed response at resonance are sufficient to correct the response over a broad range of wave periods In TEST17c the same geometry is used with the free surface pressure option FSP described in Section 10 11 The FSP surface is the same as the lid described above and the same gdf file is used as in TEST17a and 17b In the CFG file the parameter IMODESFSP 1 is used to select the subroutine PRESSURE FS in the NEWMODES DLL file and NMODESFSP 1 The pressure distribution on the FSP surface is constant To correspond with the original Test17 the pressure represented by mode 7 is set equal to zero by assigning mode 7 to be fixed in the file test17c frc Input file TEST17 CFG file cylinder with moonpool ipltdat 5 ilowgdf 5 ILOWHI 1 IALTFRC 1 ISOLVE 1 PANEL_SIZE 0 2 IPERIN 3 IPEROUT 3 NUMHDR 1 Input file TEST17 cylinder with moonpool NPATCH 3 0 do Ap OOOO OO go Ooo 61 100000 350000 600000 650000
400. ry defines the outer rectangular boundary of the control surface and the other three are required to separate the waterlines in quadrant one Note that partition 2 starts at the origin in this case without a segment along the y axis since only half of the middle column is in the first quadrant and the images of both the body and partition form a closed waterline and partition As in Example 3 the outermost points do not need to intersect the outer boundary the program extends or reduces the first and last segments automatically to intersect the outer boundary the inputs 50 0 are replaced by 60 0 For the last vertex 150 0 the X coordinate could be replaced by any value greater than 90 0 All four partitions obey the counter clockwise rule with respect to their domains Also note that they completely define the interior free surface without gaps or overlap In this example if only the horizontal drift forces and vertical drift moment were required one could assign NPATCSF 1 and NPART 1 and omit all but the first partition The view of this control surface from above the free surface is shown in Figure 11 2 11 14 Figure 11 2 View from above the free surface showing one quadrant of the control surface described in Example 4 The rectangular outer boundary and partition boundaries are represented by the heavy dashed lines Gaps between the partition boundaries are included for clarity
401. s 17 IBO DY is out of range In a multi body problem each IBODY must bein the range 1 to NBODY This error would probably indicate a bug in WAMIT s writing of RGKINIT TXT 18 Two or more bodies have the same IBODY In a multi body problem the IBODY s must be distinct This error would probably indicate a bug in WAMIT s writing of RGKINIT TXT C 20 19 A surface has a patch type that is invalid for analysis Patch types are controlled by color coding for example color 11 bright cyan is reserved to indicate a dipole patch Color 15 bright white is reserved for exterior free surface patches these are excluded from both low order and higher order analysis Review the colors of your surfaces don t use color 15 20 Demo version used with non demo model file Wamit Inc distributes two different versions of rg2wamit dll both with the same filename The demo version is restricted to only function with a few specific model files and is freely distributed The real version is only distributed to users who are licensed to use WAMIT and MultiSurf together This error occurs when the demo version of rg2wamit dll is used with a M ulti Surf model file other than one of the authorized demo files Using WAMIT RGKernd Interfacel doc C 21
402. s TORUS2 Two concentric toroids with elliptical sections The dimensions of each toroid are as defined in subroutine TORUS_ELLIP above It is required that RAXISI1 gt RCIRC1 and RAXIS2 gt RAXISI RCIRC1 RCIRC2 i e there is a circular free surface in the center of the inner torus and also an annular free surface between the toroids CIRCCYLH First quadrant of a circular cylinder with a horizontal axis in the free surface RADIUS and HALFLEN are the radius and half length of the cylinder If NPATCH 3 the interior free surface is included for use with IRR 1 FPSOINT FPSO with internal tanks of rectangular shape as illustrated in TEST22 The dimensions and representation of the hull are the same as in subroutine FPSO2 described above XBODY 3 is the height of the body coordinate system which must be consistent with the input in the POT file XVER is the array of vertex coordinates for each tank input in the same format as in Section 7 5 The FPSO and tanks are symmetric about the Y 0 plane ISX 0 ISY 1 Patches 1 7 represent the hull and 8 10 represent the interior free surface if IRR 1 as in FPSO2 One half of each tank is represented by 4 additional patches or 5 additional patches if the tank is closed on the top CIRCCYL_ARRAY First quadrant of a rectangular array of circular cylinders with radius RADIUS draft DRAFT and horizontal spacing ASPACE between the centers in the X and Y directions The array is symmetric about X 0 and Y 0 NX
403. s These requirements are best understood in the context of the procedure used by the program to define the waterline contour from the data in the GDF file As the first step for the automatic discretization of the free surface the program searches for and identifies all of the waterline segments between the panel vertices which are in the plane of the free surface or within a specified small distance of this plane If the nondimensional absolute value of the vertical coordinate is less than TOL 1 E 5 the vertex is defined to be in the plane of the free surface To avoid including very small segments which would produce a nonuniform discretiza tion waterline segments are neglected if their lengths are smaller than a specified minimum length The minimum length for this purpose is the product of another prescribed tolerance TOL 10E 3 times the average length of the waterline segments In computing this av erage length segments which are very small are neglected The program then rearranges the waterline segments in consecutive order based on testing the distance between the end 10 4 points of the segments If this distance is less than the product of TOL times the average length the program assumes the two segments are contiguous When there is a gap larger than this product the program outputs the error message Waterline panels do not form a closed contour The parameter TOL TOLGAPWL can be modified in the configuration files as e
404. s represented by panels in the same manner as conventional body panels Section 6 1 Figure 6 2 shows a typical example of a floating spar with thin helical strakes This structure is analyzed in Test Run 09 described in the Appendix Section A 9 Figure 6 2 Perspective view of a floating spar with three helical strakes showing the conventional panels on the spar and dipole panels on the strakes 6 8 The velocity potential on the dipole panels is represented by dipoles alone with no corresponding sources The unknown is the difference of the velocity potential on the two sides which is proportional to the pressure jump across the panel Since both sides of the dipole panels adjoin the fluid the direction of the normal vector is irrelevant A positive difference of the velocity potential is defined to act in the normal direction to the surface from the side on which the vertices are in the counter clockwise direction to the opposite side The order of the vertices in the GDF file is arbitrary as long as they are in a logical sequence to form a closed quadrilateral with contiguous sides The indices of the dipole panels are defined in the CFG file by including one or more lines starting with NPDIPOLE followed by the indices or ranges of indices of the dipole panels as explained in Section 4 7 In this case the format of the GDF file is as explained for the case without dipole panels in Section 6 1 and the parameter NPAN is the tot
405. s the interior free surface The default value is IRR 0 ISCATT is an integer parameter specifying whether the diffraction or the scattering prob lem is solved to obtain the diffraction potential The diffraction potential may be solved by the equation 15 12 which we define as the diffraction problem Alternatively in the scattering problem the scattered potential is solved by 15 13 and the diffraction potential is obtained from equation 15 8 This option is only available in the low order method ILOWHI 0 ISCATT 0 Solve the diffraction problem ISCATT 1 Solve the scattering problem The default value is ISCATT 0 ISOLVE is an integer parameter specifying the method of solution for the linear systems in POTEN These three alternative methods are described in Section 14 2 ISOLVE 0 Use the iterative solver ISOLVE 1 Use the direct solver ISOLVE N N gt 2 Use the block iterative solver with N blocks ISOLVE 1 Special value used for wavemakers in planes of symmetry See Section 12 3 The default value is ISOLVE 0 ISOR is the integer used to specify whether the source strength is evaluated ISOR 0 Do not evaluate the source strength ISOR 1 Evaluate the source strength The default value is ISOR 0 The source strength is required in the low order method ILOWHI 0 if FORCE evaluates the fluid velocity on the body IOPTN 5 2 or 3 the pressure free surface elevation or velocity in the fluid domain by the sour
406. s are close to each other and to the free surface Further details are given in Section 15 3 15 3 DISCRETIZATION OF THE INTEGRAL EQUATIONS IN THE LOW ORDER METHOD ILOWHI 0 The mean position of the body wetted surface is approximated by a collection of quadri laterals Each quadrilateral is defined by four vertices lying on the body surface Their Cartesian coordinates are input to WAMIT They are numbered in the counter clockwise direction when the panel is viewed from the fluid domain Instructions on how to input the vertex coordinates are given in Chapter 6 In general the quadrilaterals defined above are not plane but if a sufficiently fine dis cretization is used for a boundary surface with continuous curvature each element will approach a plane surface In this circumstance a plane approximation of the general quadrilateral is defined by the midpoints of each side which always lie in the same plane Each panel is defined by projecting the four vertices onto this plane If the coordinates of two adjacent vertices coincide the quadrilateral panel reduces to a triangular panel For bodies of general shape gaps may exist between panels Experience suggests that they do not significantly affect the accuracy of the velocity potential and the hydrodynamic forces The radiation and diffraction velocity potentials are taken to be constant over each panel The discretization errors associated with the selection of plane panels and a piecewi
407. s defined below and the complete CSF file should be of the following format 1 ILOWHICSF ISXCSF ISYCSF NPATCSF ICDEF PSZCSF RADIUS DEPTH NPART NV 1 X 1 1 Y 1 1 X 1 2 Y 1 2 X 1 NV1 Y 1 NV1 NV 2 X 2 1 Y 2 1 X 2 2 Y 2 2 X 2 NV2 Y 2 NV2 NV NPART X NPART 1 Y NPART 1 X NPART 2 Y NPART 2 X NPART NV1 Y NPART NV1 11 10 The symmetry indices ISXCSF and ISYCSF of the control surface must be the same as the symmetry indices ISX ISY of the body Here the body symmetry indices ISX ISY are the same as the inputs in the GDF file except in the case where the body is trimmed Special attention to symmetry is required if the body waterline is trimmed since this may affect the symmetry of the body If the trim includes a roll angle XTRIM 3 is nonzero and ISY 0 regardless of the GDF input symmetry index In this case ISYCSF 0 must be specified in the CSF file Similarly if the trim includes a pitch angle XTRIM 2 is nonzero and ISXCSF 0 must be specified For cases where NBODY gt 1 and one or more bodies have planes of symmetry as specified in the GDF file and no trim angles are specified for the body then the same planes of symmetry should be specified for the control surface regardless of the fact that no symmetry is used for the potential solution In this case the control surface is reflected in the same manner as the body Tests 05 and 13 are examples of this convention If incorrect symmetry indi
408. s the fin represented by a dipole patch on the positive Y axis If NPATCH 3 the side of the cylinder in quadrant 2 is also represented If RADIUS 0 and NPATCH 1 the cylinder is omitted and the subroutine defines the upper half of a single fin extending from Y WIDTH to Y WIDTH INONUMAP is optional with default value 0 If INONUMAP 1 is input the discretization on the fins is finer near the outer ends using a cosine spacing transformation CYLFIN4 defines a circular cylinder with 4 symmetric fins represented by dipole patches in the planes X 0 and Y 0 DRAFT is the draft The other dimensions and parameter INONUMAP are as defined for CYLFIN above Arbitrary combinations of ISX and ISY can be specified The number of patches is equal to 4 with two planes of symmetry 6 with one plane of symmetry and 9 with no planes of symmetry The last patch is on the bottom and can be omitted if the cylinder is bottom mounted SKEW_SPHERE defines two quadrants of a floating skewed hemisphere The center plane of the body is inclined at the position X SKEW Z Patch 1 represents the body surface and patch 2 can be used to represent the interior free surface if IRR 1 ISX 0 and ISY 1 CIRCCYL_NOSYM defines the entire surface of a circular cylinder Patch 1 represents the side and patch 2 represents the bottom of the cylinder If IRR 1 the internal free surface is represented by patch 3 If NPATCH 1 and DRAFT gt 1 E 8 the cylinder is considered to be bottom moun
409. s used to derive the gravitational restoring moment of the body In any situation where this assumption is not satisfied due to the presence of an external vertical inertia force the gravitational restoring moment should be corrected for this difference via the stiffness matrix EXSTIF The units of EXMASS EXDAMP EXSTIF must correspond to those used to specify the fluid density RHO and the length ULEN with time measured in seconds These matrices must be defined with respect to the body fixed coordinate system It is also possible to use Alternative Form 2 with the external force matrices in separate files In this case the index IMASS IDAMP and or ISTIF is set equal to 2 and followed by the corresponding file name header IOPTN 1 IOPTN 2 IOPTN 3 IOPTN 4 IOPTN 5 IOPTN 6 IOPTN 7 IOPTN 8 IOPTN 9 RHO XCG YCG ZCG 2 MASS file name containing inertia matrix 2 DAMP file name containing damping matrix 2 STIF file name containing stiffness matrix NBETAH BETAH 1 BETAH 2 BETAH NBETAH NFIELD XFIELD 1 1 XFIELD 2 1 XPIELD 3 1 XFIELD 1 2 XFIELD 2 2 XFIELD 3 2 XPIELD 1 3 XFIELD 2 3 XFIELD 3 3 XFIELD 1 NFIELD XFIELD 2 NFIELD XFIELD 3 NFIELD MASS is a file name which contains external inertial forces to the bodies and interactive inertial forces between bodies For example the data in MASS for a body are listed below header EXMASS 1 1 EXMASS 1 2 EXMASS 1 6 NEWMDS EXMASS 2 1 EXMASS 2 2
410. same unique filename providing an efficient system for preserving output files without the need for interactive input during the runs If IOUTLOG 1 is assigned the log file wamitlog txt is copied at the end of the run to a second file with the same filename as the OUT files ending in _log to provide an archive of the inputs for the run In the Windows PC environment filenames are not case sensitive A distinction must be made for systems such as UNIX and LINUX which are case sensitive Most filenames and extensions which are assigned by WAMIT are specified in lower case letters via assign ments of type CHARACTER in the source file modulesc f This applies in particular to the input files fnames wam and config wam and to the extensions p2f out etc The only exceptions to this convention are the scratch files opened temporarily by WAMIT with the explicit names SCRATCHA SCRATCHB etc Input parameters which are read by the program such as the parameters in the configuration files are not case sensitive The extensions gdf pot and fre are required unless the corresponding assignments are changed in the source code A list of all reserved filenames is in Section 14 8 4 10 FILE FORMAT The free format READ statements read only the specified data on a line or on subsequent lines if there is insufficient data on the first line Comments inserted after the specified data are ignored T
411. scontinuous derivative if this is the first derivative a degree 1 breakpoint the curve typically has a knuckle A breakline is a u or v constant line across which the surface has a discontinuous derivative if this is the first derivative a degree 1 breakline the surface typically has a knuckle line at this parameter value Thus one reasonable way to build a truncated vertical cylinder is to construct a meridian curve with a breakpoint at the chine eg atype 1 BCurve or CCurve and revolve it 90 degrees about a vertical axis creating a single RevSurf covering both the bottom and sides M ultiSurf will be aware of the degree 1 breakline along the chine and will display the sharp edge correctly Before WAMIT version 6 4 we had to recommend in general that breaklines not be used on surfaces intended for WAMIT consumption WAMIT was not be aware of the breakline and would have been modeling a smooth continuous distribution of potential across the chine In the version of RG2WAMIT released with WAMIT version 6 4 breaklines are automatically taken into account A MultiSurf surface with N u constant degree 1 breaklines and M v constant degree 1 breaklines is split along these breaklines into N 1 x M 1 panes and is presented to WAMIT as that many separate patches This all takes place under the hood with little need for the user to be aware of it The splitting at breaklines will be visible in the patch counts seen
412. se constant variation of the velocity potential are of the same order if the integration of the singular components of the wave source potential over the panels are carried out with sufficient accuracy Based on this discretization the continuous integral equations 15 11 and 15 12 can be reduced to a set of linear simultaneous equations for the values of the velocity potentials over the panels For the radiation potentials we obtain N N 2nyp x gt Dapr D gt Siz 3 15 20 k 1 k k 1 where i 1 N N being the number of panels For the total diffraction potential N 2mp x X Dikpr 4Tpo X 15 21 k 1 The matrices Dig and S are defined by Dix a E dg 15 22 Su f GE xi d 15 23 where s denotes the surface of the k th panel The collocation points x where the integral equations are enforced are located at the panel centroids The analytic integration of the Rankine source potentials and their derivatives follows the theory outlined in 2 The formulae used for the analytic integration of the logarithmic singularity are derived in 6 The integration over each panel of the regular part of the wave source potential is approximated by multiplying the value of the integrand at the centroid by the panel area 15 4 INTEGRAL EQUATIONS FOR THE SOURCE FORMU LATION In the low order method the source formulation is used to derive the fluid velocity compo nents on the body surface T
413. se parameters is as follows with explanatory comments on each line IALTFRC 3 use FRC format in Section 8 3 IALTFRCN 2 1 2 Form of FRC file for each body IGENMDS 1 1 Body 1 IGENMDS 1 IGENMDS 2 1 Body 2 IGENMDS 1 IGENMDS 3 2 Body 3 IGENMDS 2 IRR 1 2 Body 1 IRR 2 IRR 2 1 Body 2 IRR 1 IRR 3 1 Body 3 IRR 1 ITRIMWL 1 Trim waterlines for at least one body NPDIPOLE 2 5 8 Body 2 dipole patches or panels NPFORCE 1 1 4 Body 1 integrate pressure on panels patches 1 to 4 NPFSP 4 4 4 Body 4 free surface pressure patch or panel NPNOFORCE 2 5 8 Body 2 skip pressure on panels patches 5 to 8 NPTANK 1 8 11 12 15 Body 1 tank patches or panels XTRIM 1 1 0 15 0 Body 1 trim coordinates XTRIM 2 0 0 0 0 0 0 Body 2 trim coordinates XTRIM 3 5 0 0 0 10 0 Body 3 trim coordinates Some of these inputs are illustrated in the test runs TEST05 TEST13 and TEST13a described in Appendix A The array IALTFRCN specifies the value of IALTFRC for each separate body The value of each element in this array must be either 1 or 2 as in the example above If the number of elements in the configuration files is less than NBODY the remaining elements are assigned the same value as the last input Thus if NBODY is large it is not necessary to define each element of the array explicitly If IALTFRC is the same for all bodies only the first body needs to be specified in IALTFRCN The following alt
414. se the program auto matically assigns appropriate values to NU and NV on each patch with the objective that the maximum physical length of each panel is equal to PANEL SIZE This parameter is specified in the same dimensional units of length as the data in the GDF file This option is especially convenient for convergence tests where the size of all panels can be reduced simultaneously Similarly KU KV IQUO IQVO and IQUI IQVI marked by f should not be specified in the SPL file when nonzero values are assigned to KSPLIN IQUADO and IQUADI 7 28 respectively in the configuration files In this case the program sets KU and KV equal to KSPLIN IQUO and IQVO to IQUADO and IQUI and IQVI to IQUADI If these parameters are assigned in the SPL file separate assignments must be made for each patch as indicated in the above format Conversely parameters which are assigned in configuration files are global with the same value assigned to all patches and all bodies Similarly if KU KV IQUO IQVO or IQUI IQVI are included in the SPL file separate values are assigned to the u and v coordinates whereas if these parameters are assigned via global parameters KSPLIN IQUADO IQUADI the same values are used for both coordinates Experience using the higher order method indicates that quadratic KSPLIN 3 or cubic KSPLIN 4 B splines are generally appropriate to represent both the geometry and velocity potential with the former KSPLIN 3 preferred wh
415. see Chapter 7 The coordinates the extended normal vector corresponding to 6 rigid body modes and the Jacobian are output in the pnl file The value of the Jacobian at the prescribed point replaces the panel area in the format shown in Section 5 2 The pressure and the fluid velocity vector at these points are output in the files 5p 5vx 5vy and 5vz in the same format as shown in Section 5 2 If IPNLBPTO is assigned in the configuration file the alternative option is utilized with the points on the body surface specified by the user as described in Sections 4 6 and 5 5 When the above options are specified a second output file 5pb is also generated This file contains the B spline coefficients and other relevant parameters for the evaluation of the pressure and its derivatives on the body surface The total pressure coefficient 4 the diffraction pressure yp and the radiation pressure yr are output separately The radiation pressure has as many components as the number of modes specified in the POT file including generalized modes Following the definition of the nondimensional pressure Section 3 5 these three components are related by the equation p pp KLS Esp J Here K L is the nondimensional infinite depth wavenumber is the nondimensional motion amplitude and j is the mode index The total pressure coefficient is output in all cases The diffraction pressure coefficient is output when IRAD gt 1 and IDIFF gt 1 Since the
416. see Section 4 2 The program assumes that all generalized modes j gt 6 are free and sets the array elements MODE j equal to one for these modes during the computations The options in FORCE have the same effect for generalized modes as for the rigid body modes except for restrictions on the mean drift forces evaluated by direct pressure integration Option 9 and control surfaces Option 7 The two horizontal drift forces and the vertical drift moment can be evaluated including all pertinent motions of the body in the rigid body and generalized modes using the momentum analysis Option 8 Options 9 and 7 cannot be used for bodies with generalized modes In the analysis of multiple bodies NBODY gt 1 where some but not all of the bodies have generalized modes Options 9 and 7 can be used for the bodies with no generalized modes The Alternative Form 2 of the FRC file IALTFRC 2 should be used to specify the appropriate mass damping and stiffness matrices for the body including its extended modes For example in case 1 above to account for the mass and stiffness of the ship hull it is necessary to include corresponding 8 x 8 matrices which correctly specify these coefficients for the distribution of internal mass within the ship and for its bending motion 9 4 9 2 USING DEFMOD WITH THE LOW ORDER METHOD To facilitate the definition of the vectors uj vj wj by users a pre processor program DEFMOD is provided in Fortran source co
417. st07 cfg TESTO7 CFG ISSC TLP ILOWHI 0 fine discretization ipltdat 1 ISOR 1 ISOLVE 4 ISCATT 1 ILOG 1 IRR 0 MONITR 0 NUMHDR 1 IALTFRC 2 Input file test07 pot TESTO7 POT ISSC TLP ILOWHI 0 fine discretization 450 HBOT o 0 IRAD IDIFF 3 5 10 15 1 O 1 NBODY test07 gdf 0 0 0 0 1 O 1 0 1 0 First 10 lines of input file test07 gdf TESTO7 GDF ISSC TLP ILOWHI 0 fine discretization 43 125 9 806650 1 1 1012 49 09267 37 15733 0 00000 49 09267 37 15733 0 33626 50 43388 38 90522 0 33626 50 43388 38 90522 0 00000 49 09267 37 15733 0 33626 49 09267 37 15733 1 33212 Input file test07 frc TESTO7 FRC ISSC TLP ILOWHI 0 fine discretization IALTFRC 2 1 1 1 2 0 0 0 1 1 IOPTN IOPTN 4 lt 0 signifies fixed modes 6 NDFR 110001 IMODE 1 RHO 0 0 3 0 XCG 1 IMASS 53066 4 0 0 0 159199 2 O 0 53066 4 O 159199 2 0 O 0 O 53066 4 0 0 O O 159199 2 O 8 0201552E7 0 O 159199 2 O 0 0 8 0201552E7 O 0 0 0 0 O 9 54906731E7 0 IDAMP 0 ISTIFF 0 NBETAH 0 NFIELD A 8 ELASTIC COLUMN WITH GENERALIZED MODES TEST08 This test run evaluates the force coefficients and RAO s for a bottom mounted vertical cylinder of circular cross section with four bending modes defined by shifted Jacobi poly nomials The hydroelastic analysis of these bending modes is analyzed using the generalized body mode option described in Chapter 8 Further details are given in Referenc
418. static coefficients In general these are defined by the matrix Reference 13 equation 2 17 Cij pg n w 2D dS 9 11 Here D denotes the divergence of the vector u v w assumed to be continuous in the vicinity of the body surface In cases where D 0 the hydrostatic matrix can be evaluated uniquely from the vertical component w For these cases the simplified hydrostatic matrix Cij pg JI nj w dS 9 12 is computed and no further steps are required by the user This computation is performed in DEFMOD if that program is used or internally in WAMIT if the DLL subroutine NEWMODES is used In special applications where D 4 0 the hydrostatic coefficients can be programmed specially by modifying the code in the main program of DEFMOD Alternatively the extra contribution from the last term in 9 11 can be included as an external force in the stiffness matrix of the FRC file The hydrostatic coefficients c are output as part of the complete hydrostatic matrix in the file out hst with the format indicated in Section 5 6 Here out denotes the filename of the out file for the run Note that the hydrostatic coefficients associated with generalized modes do not include gravitational restoring due to the internal mass of the body Nonzero restoring effects due to gravity should be included as external force components in the stiffness matrix of the FRC file The coupling between the generalized modes and betw
419. t value is NUMNAM 0 PANEL SIZE is a parameter used for automatic subdivision of patches in the higher order panel method Further information is given in Chapter 7 PANEL SIZE lt 0 0 subdivide patches into panels as specified by the parameters NU NV 4 34 in the SPL file PANEL SIZE gt 0 0 subdivide patches into panels so that the maximum length of each panel is approximately equal to the value of this parameter in dimensional units The default value is PANEL_SIZE 1 0 RAMGBMAX is the number of Gigabytes of RAM available for use as scratch mem ory Instructions for using this parameter are given in Section 14 3 The default value is RAMGBMAX 0 5 This parameter replaces the parameter MAXSCR in Version 6 RHOTANK is a real array used to specify the density of fluid in internal tanks The density specified is relative to the density p of the fluid in the external domain outside the bodies The data in the array RHOTANK must be input in the same order as the data in the array NPTANK Multiple lines of this parameter may be used with an arbitrary number of data on each line but each line must begin with RHOTANK The total number of tanks NTANKS is derived from the inputs NPTANK in the POTEN run If fewer than NTANKS values of RHOTANK are specified the remainder of the array is assigned the last non negative value Thus if the density is the same for all tanks only the first value is required Zero may be assigned but negat
420. tate input of user defined data and the output of error messages The body index IBI is useful for multiple body computations where different generalized modes may be specified on each body If NBODY 1 the index IBI 1 For the analysis of a single body the mode index 7 is assigned consecutively as explained after equation 9 1 with the first generalized mode j 7 and the last generalized mode j 6 NEWMDS 1 For multiple bodies the arrays for each body are concatenated in succes sion The vector IBMOD 1 NBODY points to the last mode index j used for the preceding body Thus in general for body IBI the first generalized mode is j J BMOD IBI 7 and the last generalized mode is j IBMOD IBI 6 NEWMDS IBI Thus the pointer IBMOD is useful to assign generalized modes correctly when multiple bodies are analyzed The patch panel index IPP can be used to identify specific portions of the body IPP is the local panel or patch number of the body as listed in the corresponding GDF file When NEWMODES is used to define generalized modes the input IGENMDS must be specified in the configuration files with a nonzero value Different values of IGENMDS can be useful in NEWMODES to identify different subroutines of the library This is illustrated in the version supplied with WAMIT where the integers 16 17 18 are used to identify the corresponding test runs and associated subroutines The input IFLAG is generated internally by the calling routi
421. tating that the waterline is not closed In that case a larger value of TOLGAPWL should be input in the CFG file TEST1 Ea pig C He ae Figure 10 2 Automatic discretizations on the interior free surface for various higher oder test runs corresponding to the inputs described in Appendix A but with IRR 3 See also the perspective figures for Test13a in Appendix A In Test15 two patches are required on the middle columns due to the symmetry plane x 0 whereas the other interior free surfaces are covered by a single patch In Test22 the interior free surface covers the entire interior of the waterlit but it is obscured by the forward tank 10 5 ASSIGNING DIFFERENT VALUES OF IRR FOR NBODY gt 1 It is possible to use different values of IRR for each body in a multibody analysis The definition of IRR for each body is the same as in Sections 10 1 10 4 The format for inputting different values of IRR for each body in the CFG file is shown in Section 8 4 If the same value of IRR is used for all bodies it is not necessary to use the notation IRR n and one scalar value with the notation IRR can be input If the special notation IRR n is used in the CFG file it is recommended to input values for each body explicitly even if IRR 0 for some bodies The order of these inputs is arbitrary However this procedure is not required If less than NBODY values of IRR n are included in the CFG file the rules are
422. te effectively the tangential components of the fluid velocity on the body and hence the second order mean pressure the solution for the velocity potential based on Green s theorem is augmented if ISOR 1 by the corresponding solution for the source distribution on the body surface A brief description of the theory is provided in Section 15 4 Further details are given in 10 and 26 Setting the parameter ISOR 1 in the configuration files specifies that the source distribution integral equation is solved in addition to the velocity potential integral equa tion This is required in some cases for Options 5 6 7 and 9 in the FRC file as noted in Section 4 3 Values of the drift force and moment can be compared with the corresponding outputs evaluated using momentum conservation Option 8 and with the drift forces evaluated using the control surface Option 7 In general the results obtained from integration of the second order pressure will require a finer discretization on the body surface particularly in the vicinity of sharp corners Body symmetries can be exploited to minimize computing time Special attention must be given to the evaluation of the drift forces since these are dependent on quadratic products of the first order solution For example if the body has two planes of symmetry the vertical first order exciting force and heave response can be evaluated simply by setting IRAD 1 IDIFF 0 MODE 3 1 and the remaining MODE in
423. te the output files gdf PAN DAT and gdf PAT DAT used for plotting the panel and patch discretizations see Section 5 7 IPLTDAT 0 Do not generate the output files gdf PAT DAT and gdf PAN DAT IPLTDAT gt 1 Generate the output files gdf PAT DAT and gdf PAN DAT for plotting the panel and patch discretizations with IPLTDATxIPLTDAT subdivisions The default value is IPLTDAT 0 IPNLBPT is an integer parameter specifying the option to evaluate the body pressure at specified points x y z listed in the input file gdf BPI IPNLBPT 0 output the body pressure at the panel centroids or on a uniform parametric mesh in the higher order method IPNLBPT gt 1 output the body pressure at the points listed in the input file gdf BPI These points are defined with reference to the body fixed dimensional Cartesian coordinates for each body IPNLBPT lt 1 output the body pressure at the points listed in the input file gdfBPI These points are defined with reference to the global coordinate system The default value is IPNLBPT 0 When IPNLBPT 40 and ILOWHI 0 the absolute value of IPNLBPT specifies the number of panels nearest to each point specified in gdf BPI See Section 4 6 for further details IPOTEN is an integer parameter specifying if the POTEN subprogram is executed during the WAMIT run IPOTEN 0 Do not execute POTEN IPOTEN 1 Execute POTEN The default value is IPOTEN 1 IQUADI is an integer parameter specifying the order of t
424. ted and DRAFT must be equal to the parameter HBOT in the POT file If NPATCH 1 and DRAFT lt 1 E 8 the cylinder is considered to be of zero draft and patch 1 represents the bottom If INONUMAP 1 nonuniform mapping is used on the side and bottom with finer discretization near the corner and waterline The center of the waterplane of the cylinder is located at the position XS YS ZS relative to the body coordinate system ELLIPSOID_NOSYM_TANK 4 quadrants of ellipsoidal body with one tank no planes of symmetry A B C are the semi axes of the ellipsoid The center of the ellipsoid is at XS YS ZS with respect to the body coordinate system XL XB XD are the length width and depth of the tank The center of the tank free surface is at the position SL SB SD relative to the center of the ellipsoid The center of the ellipsoid must be in the plane of the free surface only the lower half is represented BARGE_INT defines the first quadrant of a rectangular tank equivalent to the interior surface of a rectangular barge HALFLEN is half the length HALFBEAM is half the width and DRAFT is the tank depth BARGENUC defines the first quadrant of a rectangular barge with extra nonuniform patches near the corners at the ends The inputs are the same as for subroutine BARGE as defined above except for the additional parameter STRIP Extra patches are added within strips of width STRIP on the end side and bottom which adjoin the corners at the end The mapping
425. test18 gdf TEST18 GDF vertical cylinder bottom mounted 1 0000 9 80665 ulen grav 1 1 isx isy des npatch igdef 2 NLINES 10 0000 200 000 radius draft 0 uniform mapping Input file test18 spl TEST18 spl bottom mounted cylinder R 10 T 200 npatch 1 4 8 NU NV Patch 1 side u azimuthal v vertical Input file testi8 frc TESTO8 FRC file vertical column with 4 bending modes 1 1 1 1 0 0 0 o 0 1 0 0000000 0000000 1 000000 1 0 0 0 O O 0 O O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 0 O O 0 O O O 0 O 0 O O O 0 69115 62832 62832 62832 O 0 O O 0 O 62832 67320 62832 62832 0 0 0 O O 0 62832 62832 663283 62832 O 0 O O O 0 62832 62832 62832 65688 0 1 O 0 O O 0 O 0 O 0 0 O 0 O O 0 O 0 O 0 0 O 0 0 O O 0 O O 0 0 O 0 O O O 0 O O 0 0 O 0 O O 0 O 0 O 0 0 O 0 O O O 0 O O O O 0 0 O O 0 O 103044 412177 824354 1339575 0 0 O O O 0 412177 4430902 9789203 16487078 O 0 O O O 0 824354 9789203 37899671 64382041 0 0 O O O O 1339575 16487078 64382041 162406554 A 19 CATAMARAN BARGE TEST19 The geometrical configuration is the same as the barge near a wall TEST04 Since only head seas are considered the hydrodynamic outputs correspond to TEST04 except for the different definition of the incident wave amplitude which applies for a bod
426. th of the symmetry planes x 0 and or y 0 Wavemakers with prescribed normal velocities are located in the walls The opposite walls of the wave tank are assumed to have absorbing beaches represented here by open domains extending to infinity In all cases it is assumed that the wall s are planes of symmetry and the fluid motion is symmetrical about these planes Thus the solution for the velocity potential in the fluid domain can be represented by a distribution of sources of known strength proportional to the normal velocity of the wavemaker and it is not necessary to solve the integral equation for the velocity potential on the wavemakers This saves considerable computational time and also avoids the singular solution that would otherwise occur for bodies of zero thickness in the plane of symmetry The geometry of each wavemaker is defined in the gdf file In the low order method ILOWHI 0 a sufficient number of panels must be included on each wavemaker to ensure a converged solution In the higher order method ILOWHI 1 only one patch is required on each wavemaker If the wavemakers are rectangular or quadrilateral the higher order analysis can be carried out most easily using the option IGDEF 0 as explained in Section Told The parameter ISOLVE 1 is used in the configuration files to indicate that the wave makers are in planes of symmetry and that the solution of the integral equation is not re quired Suitable generalized modes
427. the added mass and damping coefficients evaluated by WAMIT in Option 1 To displace the body in calm water in mode j with time varying acceleration t the component i of the force required to oppose the hydrodynamic pressure is given 29 by Fi t Ag oo amp t f Lisl amp t 7 dr 13 1 where A 00 is the infinite frequency limit of the added mass The radiation IRF Li t is evaluated from either the Fourier cosine or sine transforms 13 5 6 These IRFs are output from F2T in the files IR 1 JR 1 and KR 1 as explained below in Section 13 4 The exciting forces and RAOs are of the diffraction type evaluated by WAMIT in Options 2 3 and 4 and defined relative to an incident wave of uniform amplitude A propagating in the direction 5 The corresponding IRFs are defined with respect to an impulsive incident wave moving in the same direction where the free surface elevation n x y t is equal to a delta function t at the origin x y 0 Further details are given n 26 and 30 Here we define a general output U t to be either the exciting force or the RAO with respect to the mode i It follows that Ut KdT n 0 0 t 7 dr 13 2 The IRFs Ki t are evaluated from the Fourier transform of the frequency domain exciting force or RAO using 13 10 These IRFs are output from F2T in the files IR n and JR n where n 2 3 4 as explained below in Section 13 4 13 2 ACQUIRING INPUT DATA FOR F2T WITH WAMIT The frequen
428. the free surface This simplifies the definition of the control surface especially for bodies with complicated geometry of the waterline In addition the numerical errors are generally smaller for field points that are not too close to the body surface This simplification is illustrated in Test22 as described in Appendix A 22 If thin submerged elements are represented by dipole panels or patches the mean drift force and moment cannot be evaluated by direct pressure integration on the body The alternative method using a control surface is valid in this case with some exceptions If the dipole elements are entirely below the free surface both Alternatives 1 and 2 can be used If the dipole elements intersect the free surface as in the case of the spar with helical strakes shown in Appendix A 21 Alternative 1 must be used and only the horizontal drift force and vertical drift moment can be evaluated correctly The drift force and moment evaluated using a control surface are defined in terms of the body coordinates as in the case of direct pressure integration The control surface can be defined using MultiSurf as explained in Appendix C The mean drift forces can be evaluated using control surfaces without evaluating the mean drift forces using pressure integration Option 9 If the low order method is used ILOWHI 0 it is not necessary to use the source formulation However the potential formulation ISOR 0 may give inaccurate results
429. the geometry after trimming using the data files which are defined by the parameter IPLTDAT in the CFG file to ensure that the actual trimmed structure is correct Except for the GDF coordinates the definitions of coordinate systems etc are as defined in earlier chapters In particular the body motions and forces are defined with respect to the conventional body coordinates x y z Thus for example surge is in the horizontal direction and heave is in the vertical direction relative to the free surface Rotations and moments are defined with respect to the origin of this coordinate system XBODY 1 XBODY 2 XBODY 3 are the X Y Z coordinates of the origin of the body coordinate system relative to the global coordinate system and XBODY 4 is the angle in degrees of the x axis relative to the X axis of the global system in the counterclockwise sense as Shown in Figure 6 2 The mass and inertia parameters in the FRC file are defined with respect to the body coordinates and apply to the trimmed configuration as if it was the original input for the 12 7 run The outputs in the MMX file can be checked to verify that these are correct in the body coordinate system The input parameter XTRIM 1 which defines the vertical coordinate z of the origin of the GDF coordinates is in the same units as the dimensional GDF coordinates cor responding to the parameter GRAV in the GDF file The angles XTRIM 2 pitch and XTRIM 3 roll are in
430. tion on the bottom Several examples of csf files are included below to illustrate the use of partition boundaries Header lines are omitted for brevity Example 1 single waterline with circular outer boundary as in TEST05c and TEST 13c ILOWHICSF ISX ISY 1 NPATCSF ICDEF PSZCSF 22 2 RADIUS DEPTH NPART Example 2 single waterline with quadrilateral outer boundary as in TEST05s and TESTI3s ILOWHICSF ISX ISY NPATCSF ICDEF PSZCSF RADIUS DEPTH NPART NV 1 ONNWwWHOO HA or SO O woo 2 0 0 2 0 3 0 0 3 X Y coordinates of three vertices Note in Example 2 the partition boundary is specified only in quadrant one since ISX 1 and ISY 1 The first vertex is on the x axis the second vertex is above the first and the third vertex is on the y axis to close the partition and surround the body waterline The order of the vertices is such that they follow a counter clockwise progression around the body with increasing polar angle relative to a point inside the body 11 12 Example 3 TLP or semi sub with four columns and two planes of symmetry with a circular outer boundary as in TESTO7 and TEST14 1 ILOWHICSF 1 1 ISX ISY 0 O 10 NPATCSF ICDEF PSZCSF 85 0 40 0 RADIUS DEPTH 1 NPART 3 nvi 0 0 50 0 0 0 0 0 30 0 0 0 X Y coordinates of vertices In this case since the waterline is a closed curve in the interior of quadrant one the partition boundary is required to separate the waterline in quadrant one from th
431. to automate the conversion of old input files Chapter 5 describes the output files which contain the principal data computed by the program as well as log files error files and auxiliary files which provide useful information regarding the geometry of the structures Chapter 6 describes topics which are specific to the low order method These include the low order Geometric Data File GDF which defines the coordinates of panel vertices the use of the source formulation to evaluate the fluid velocity and second order mean pressure on the body surface and the analysis of bodies with thin elements such as damping plates or strakes Chapter 7 describes topics which are specific to the higher order method including the subdivision used to represent the body surface and velocity potential on this surface and the representation of the potential in terms of B splines Alternative methods for defining the body geometry are described including the use of low order panels the use of B splines to provide a higher order continuous definition the use of explicit analytical formulae and the use of MultiSurf geometry files Chapters 8 12 describe several extended features in WAMIT These include the analysis of multiple interacting bodies Chapter 8 the use of generalized modes of body motion which can be used to describe structural deformations motions of hinged bodies etc Chapter 9 and the use of a method to remove the effect of the irregular
432. ual Fortran Further information is provided in 23 Chapters 8 and 18 14 8 RESERVED FILE NAMES To avoid conflicting filenames users are advised to reserve the extensions gdf pot frc spl p2f out pnl fpt pre mod hst csf csp bpi bpo idf rao 1 2 3 4 5p 5vz buy 5uz 6p 6ux Buy 6vz 7 8 and 9 for WAMIT input and output Other reserved filenames are config wam fnames wam break wam errorp log errorf log wamitlog txt SCRATCH where A B C 0 as well as wamit exe defmod f defmod exe the DLL files geomxact dll and newmodes dl1 and the Intel DLL files listed in Section 2 1 which are required to execute the program The utility f2t exe described in Chapter 13 uses the reserved file inputs f2t 14 10 14 9 LARGE ARRAYS OF FIELD POINTS Starting in WAMIT Version 7 1 there are two alternative options NFIELD LARGE 0 and NFIELD LARGE 1 to evaluate the pressure and velocity at field points FORCE Option 6 In the default case specified by the configuration parameter NFIELD_LARGE 0 these outputs are computed in the main loop over all wave periods together with all of the other outputs This is the same procedure as in all previous versions of WAMIT This procedure is efficient in most cases especially if multiple processing is used NCPU gt 1 and the number of wave periods NPER is large The computing time is minimized by pre computing the Rankine components of the influence functions which are independent
433. uated in the same manner After an appropriate normalization of the length and use of local coordinates with the origin at uy vy the integral takes the form Dn E aay dudo 15 36 where A u v is regular function x u v is the distance between the source and field points in physical space Ox Ox Ox Ox For simplicity we consider only the case where lol 1 J 1 and du Ju v u but the analysis below can be applied directly to a mid case Since x vu v2 is regular and thus 15 36 can be expressed in the form j L J JW dud 15 37 a 2 i where f u v is regular The singularity at the origin is removed by subdividing the square domain into 4 isosceles triangles with a common vertex at the origin and evaluating the integral separately over each triangle For example the integral over a E with a side on u 1 is vei du f E EA 15 38 ne After the change of variables u p v pq we have fa pf a Ae feet 15 39 After adding the contributions from other three triangles we have f a f d Pere io P 15 40 Next we remove the square root function from 15 40 By change of the variables q sinh as we have 1 1 T af dp ds f p psinhas f psinhas p 15 41 ee where a sinh 1 The integral 15 41 is evaluated by applying the Gauss Legendre quadrature in p and s coordinates The integral of the log singularity in the free surface component of the source pot
434. uced by each subprogram Filename pot p2f errorp log errorf log Program POTEN POTEN FORCE wamitlog txt POTEN FORCE fre out frenum gdf _pan dat gdf pat dat gdf pnl gdf hst rgklog txt frefpt gdf idf gdf bpo gdf low gdf gdf csf dat gdf low csf FORCE FORCE POTEN POTEN FORCE FORCE POTEN FORCE FORCE POTEN FORCE POTEN FORCE FORCE Description P2F File binary data for transfer to FORCE Error Log File Section 5 8 Error Log File Section 5 8 Log file of inputs Section 5 9 Formatted output file Section 5 1 Numeric output files Section 5 2 Panel data file Section 5 7 Patch data file Section 5 7 Panel data file Section 5 7 Hydrostatic data file Section 5 6 MultiSurf log file Appendix C List of field points Section 5 2 Interior free surface panels Section 10 1 Specified points for body pressure Section 5 5 Low order GDF file Section 5 7 Control surface data file Section 11 6 Low order control surface file Section 11 6 The structure of input and output files is illustrated in the flow chart shown in Figure 1 1 The filenames assigned to the various output files are intended to correspond logically with the pertinent inputs and to simplify file maintenance The primary generic data files are the two control files input to POTEN and FORCE These are referred to as the Potential Control File POT with the extension pot and 4 2 the Force Control F
435. ued by DEFMOD before overwriting an old MOD file with the same name No warning message is issued by WAMIT before overwriting an old PRE file with the same name 9 3 USING THE DLL SUBROUTINE NEWMODES The source code for the DLL file NEWMODES F is provided with the WAMIT software to facilitate the specification of generalized modes by users Users can compile their modified versions of NEWMODES following the instructions below This procedure is analogous to the modification of the DLL file GEOMXACT as described in Section 7 9 The file NEWMODES F includes the main subroutine NEWMODES and a library of specific subroutines used for different applications The library can be modified or extended by users to describe generalized modes for other applications In all cases the calls to these specific subroutines are made from NEWMODES Thus the user has the capability to make appropriate modifications or extensions and to implement these with the executable version of WAMIT The principal inputs to NEWMODES are the Cartesian coordinates X Y Z of a point on the body surface specified in the vector form X 1 X 2 X 3 and the corresponding components of the unit normal vector XN at the same point These inputs are provided by the calling unit of WAMIT and the user does not need to be concerned with providing these inputs The principal outputs which the user must specify for each generalized mode in an appropriate subroutine are 1 the symmetry i
436. uency removal option is used IRR gt 1 the computations for PER lt 0 are performed with IRR 0 If NPER lt 0 a special convention is followed to assign a total of NPER wave periods frequencies or wavenumbers with uniform increments starting with the value equal to PER 1 and using the increment equal to the value shown for PER 2 In this case only two values PER 1 PER 2 should be included in the POT file This option is convenient when a large number of uniformly spaced inputs are required The two following examples show equivalent sets of input data in lines 5 and 6 of the POT file 8 NPER 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 PER array and 8 NPER 1 0 1 0 PER 1 increment This convention is applied in the same manner for all IPERIN values irrespective of whether PER represents the wave period frequency or wavenumber Special attention is required when zero period or zero frequency inputs are required following the definitions as specified above For the example described in the preceding paragraph with IPERIN 2 the inputs NPER 4 and PER 1 1 will result in the sequence of wave frequencies equal to zero infinity 1 2 4 9 NBETA is the number of incident wave headings to be analyzed in POTEN NBETA must be an integer The following alternatives can be used NBETA 0 There are no incident wave heading angles IDIFF 1 NBETA gt 0 Execute the hydrodynamic analysis for NBETA wave angles BETA NBETA lt 0 E
437. ull surfaces are included hydrodynamic and hydrostatic parameters which are relevant for the hull alone with no internal tanks can be computed by setting RHOTANK 0 0 When planes of symmetry are specified in the GDF file ISX 1 and or ISY 1 the tank geometry is reflected in the same manner as the hull This procedure should only be used if all of the tanks intersect the symmetry plane with half of the tank on each side of the plane For example in the case of the FPSO shown in Appendix A 22 where both tanks extend across the plane of symmetry Y 0 it is appropriate to use ISY 1 as is done in TEST22 On the other hand if there are separate tanks on each side of the symmetry plane e g wing tanks the hydrostatic and hydrodnamic coefficients for the tanks will not be physically correct This situation can be avoided by defining both sides of the hull and both tanks separately in the GDF file and setting ISY 0 12 22 TRIMMED WATERLINES WAMIT includes the option to specify a trimmed waterline for each body In the trimmed condition the static orientation of the body is shifted relative to the horizontal plane of the free surface first by a prescribed vertical elevation then by a pitch angle often referred to as the trim angle and then by a roll angle heel For a given body geometry different planes of flotation can be analyzed without redefining the geometry in the GDF file A necessary condition for this procedure to be
438. urate continuous manner by B splines as explained in Chapter 7 To run TEST 11 follow the same procedure outlined above for TESTO1 but replace 01 by 11 in all references to filenames A comparison of the results from these complementary tests is summarized in Section A 11 of Appendix A 2 6 OTHER TEST RUNS The procedure for running the other test runs is the same as explained above except for copying the appropriate files to fnames wam from the original versions test wam where is the test number Alternatively runwamit test will perform the same functionality using the supplied runwamit bat file A special batch file runtests bat is included in the licensed version and a similar file rundemo bat in the demonstration version Executing the corresponding batch file command will run all of the tests in succession The display shown on the monitor gives some indication of the progress through the set of runs from test01 to test25 The entire set of runs may take several minutes depending on the computer 2 7 USING MULTIPLE PROCESSORS In Version 7 parallel processing can be performed on systems with multiple processors CPU s also known as cores Depending on the inputs and hardware the total run time 2 8 can be reduced substantially If the system includes more than one CPU open the file config wam with a text editor The default settings in this file are as follows NCPU 1 RAMGBMAX 0 5 USERID_PATH w
439. urface consists of one or more free surfaces on which the pressure distribution is specified instead of the normal velocity These are referred to as free surface pressure surfaces FSP Practical examples of bodies with FSP surfaces include oscillating water columns used for wave energy conversion and air cushion vehicles which are supported by positive mean pressure acting on the free surface below the body FSP surfaces can be either in the same plane Z 0 as the exterior free surface or submerged Z lt 0 below the level of the exterior free surface corresponding to a positive static pressure imposed on the surface as in the case of an air cushion vessel All FSP surfaces must be in horizontal planes corresponding to constant values of the static pressure on each surface The theory for this extension is described in Section 15 11 Examples of the use of FSP surfaces are included in Appendix A TEST17c and TEST25 The geometric definition of FSP surfaces is the same as for the other parts of the body surface defined within the same GDF input file s The panels or patches which represent FSP surfaces are specified using the parameter NPFSP in the configuration files to identify the panel or patch indices The inputs NPFSP must be in pairs denoting the first and last values of the index See Section 4 7 Multiple lines containing NPFSP N1 N2 can be used to indicate all of the FSP panels or patches for the body The oscillatory
440. urfaces Since the surface geometry is more directly accessed in the WAMIT RGKernel interface divisions and subdivisions are less important in general In Accurate mode evaluation they should have no bearing at all However in Fast mode there are still accuracy benefits in coordinating divisions between adjacent surfaces for example use the same number of divisions x subdivisions on a surface and its supporting curves where possible use matching divisions on surfaces that share a common edge 4 10 Irregular frequency removal In WAMIT s higher order solution irregular frequency removal is effected by providing additional surface patches that cover any interior portions of the plane of the free surface IRR 1 Such interior free surface patches can be part of the MultiSurf model They must be oriented with their positive normal direction consistent with the wetted patches i e if your model has all outward normals an interior free surface patch must have its normal upward Interior free surface patches must also be included in the Entity List of wetted surfaces and in NPATCH If you put them last in the Entity List you can easily run WAMIT with and without irregular frequency removal just by setting NPATCH appropriately in the GDF file 4 11 Coordinate singularities A coordinate singularity is a place on a parametric surface where the cross product ox u x Ox dv vanishes This can occur because either 6x
441. utput file from MultiSurf will include a filename specified by the user and the extension ms2 This file will be referred to below as body ms2 If the ms2 file is missing or cannot be found a WAMIT runtime error message Error return from subroutine RGKINIT is generated and the log file RGKLOG TXT will contain a statement that the designated ms2 file could not be opened In its simplest form the GDF input file required to run WAMIT should be in the following format header ULEN GRAV ISX ISY NPATCH 2 3 path body ms2 000 The first four lines are explained in Section 7 4 IGDEF 2 is assigned by the second integer on line 4 Line 5 contains an integer specifying the number of subsequent lines to be read from the gdf file Line 6 contains the name of the ms2 file and may include the optional path if this file is in a different directory folder The asterisk on line 7 is a default specifier to indicate that all visible surfaces in the ms2 file are to be included alternatively if only a subset of these surfaces are submerged these may be designated by following the instructions in Appendix C Line 8 includes three integer parameters with default values zero which may be used to control the accuracy of the geometry evaluation in RGKernel and also to modify the convention regarding the direction of the unit normal Further information is contained in Appendix C TEST11C and TEST20 in Appendix A are exa
442. ve normal vector in the u v plane points downward from the free surface into the body The order of the indices for the free surface patches and body patches is not restricted The subroutine CIRCCYL in GEOMXACT F is an example where the interior free surface is represented analytically as one extra patch Several other subroutines in GE OMXACT F include similar options with one or more patches on the interior free surface as explained in the headers of these subroutines When IRR gt 1 the convergence rate of the iterative solver ISOLVE 0 is reduced It is recommended to use either the block iterative solver or the direct solver The parameter ILOG in the POT file or the configuration file should be set equal to 1 when IRR gt 1 The generation of free surface patches can generally be facilitated by using MultiSurf as described in Appendix C In the low order method when IRR 1 and ISOR 0 it is recommended to discretize the interior free surface with the panels having the following properties i Panels have O 1 aspect ratio ii The length of the sides of the panels is similar to the waterline segments When ISOR 1 the interior free surface panels should be discretized in a following manner First define a set of interior panels which are contiguous with the waterline segments one panel for each segment and having aspect ratios similar to the adjoining body panels Continue this process recursively toward the centroid of the water
443. ve no effect on the READ statement so that for example the user may elect to place the twelve successive coordinates for each panel on four separate lines However the format used above is more efficient regarding storage and access time Input data must be in the order shown above with at least one blank space separating 6 3 data on the same line The definitions of each entry in this file are as follows header denotes a one line ASCII header dimensioned CHARACTER 72 This line is available for the user to insert a brief description of the file with maximum length 72 characters ULEN is the dimensional length characterizing the body dimension This parameter corresponds to the quantity L used in Chapter 4 to nondimensionalize the quantities output from WAMIT ULEN can be input in any units of length meters or feet for example as long as the length scale of all other inputs is in the same units ULEN must be a positive number greater than 1075 An error return and warning statement are generated if the last restriction is not satisfied GRAV is the acceleration of gravity using the same units of length as in ULEN The units of time are always seconds If lengths are input in meters or feet input 9 80665 or 32 174 respectively for GRAV ISX ISY are the geometry symmetry indices which have integer values 0 1 If ISX and or ISY 1 x 0 and or y 0 is a geometric plane of symmetry and the input data panel vertex coord
444. vely long in the low order method and also in the higher order method when the geometry is defined by low order panels or B splines only the first 10 lines of the GDF file are copied in these cases The maximum width of lines of data is truncated to 80 characters in wamitlog txt The existing wamitlog txt file in the directory where the program runs is overwritten with every new run If IOUTLOG 1 is assigned the file wamitlog txt is copied at the end of the run to a second file with the same filename as the OUT files ending in _log to provide an archive of the inputs for the run Otherwise if it is appropriate to save this file it should be renamed or moved to a 5 13 directory where it is protected When the input data in the FRC file is in the Alternative form 1 as described in Section 4 3 the nondimensional inertia matrix for each body is included in the file wamitlog txt This is useful when the analysis of a body is first performed using Alternative form 1 and then changed for subsequent extensions to Alternative form 2 for example when external damping is imposed on an otherwise freely floating body The normalizing factors for the nondimensional inertia matrix are the products of the fluid density and appropriate powers of the characteristic length parameter ULEN In preparing a force control file for Alternative form 2 as described in Section 4 4 these normalizing factors must be included in the inputs EXMASS when these are deriv
445. w for cases where the size of the structure is much larger than the characteristic length ULEN The default value is recommended in general If the program is unable to close a waterline using this value an error message is displayed stating that the waterline is not closed The default value is recommended in general If the program is unable to close a waterline using this value an error message is displayed stating that the waterline is not closed In that case a larger value of TOLGAPWL should be input in the CFG file The automatic CSF option should not be used for a body which is totally submerged This case can be handled more simply by using one of the GEOMXACT subroutines which represent closed bodies with an additional patch on the interior free surface as one would do to remove irregular frequencies IRR 1 This option is included in the GEOMXACT subroutines CIRCCYL ELLIPCYL SPHERE ELLIPSOID or BARGE as explained in Section 7 8 Alternatively one can use ICDEF 0 as explained above in Section 11 3 and include one or more quadrilateral patches to represent the interior free surface 11 16 11 6 OUTPUT The mean forces and moments using a control surface are output in the OUT file and in the numeric output file optn 7 or frc 7 in the same format as used for pressure integration Option 9 When IPLTDAT gt 0 in the CFG file the auxiliary file gdf_csf dat is output This can be used for visualization of the control surface using
446. waterlines see Section 4 3 and Section 4 7 e The configuration parameter NFIELD_LARGE can be used to reduce runtimes and mem ory requirements if the number of field points NFIELD is very large see Section 4 7 and Section 14 9 e The configuration parameter ICCFSP can be used to exclude or include the exter nal restoring coefficients due to the pressure in chambers above free surface pressure surfaces see Section 4 7 and Section 12 5 e The configuration parameter IREADRAO is extended to read external RAO data in either Modulus Phase or Real Imaginary forms see Section 4 7 and Section 4 13 e The parameter NPERGROUP can be used to assign multiple groups of uniformly spaced wave periods frequencies or wavenumbers in the potential control file see Section 42 1 8 Chapter 2 GETTING STARTED In this Chapter instructions are provided for installing WAMIT and making simple test runs in the PC Windows environment The basic sequence in a typical application of WAMIT is 1 prepare the input files 2 run WAMIT The principal results are then contained in output files which may be printed and post processed This architecture is illustrated in Figure 1 1 The two principal subprograms of WAMIT are POTEN and FORCE POTEN solves for the velocity potential on the body surface and optionally also for the source strength FORCE evaluates physical parameters including the force and motion coefficients and field data including th
447. waterlines such as TLP s and Semi Subs It cannot be used for bodies with internal waterlines such as moonpools This option also cannot be used for some bodies with abnormal waterlines It is strongly recommended to visualize the interior free surface using the auxiliary output files described in Section 5 7 to ensure that the representation of this surface is appropriate When IRR 3 no other changes in the inputs are required relative to IRR 0 The GDF file should specify the number of exterior body patches NPATCH not including the patches on the interior free surface The optional SPL file should also refer only to the exterior body patches After reading the GDF data the program searches for all patches which have one side in the free surface These sides are connected into closed waterlines or waterlines which end on one or two symmetry planes The waterplane interior to each waterline is divided into patches which are bounded by the vertices of the exterior patches on the waterline and by an interior axis on or near the center of the waterplane The interior patches are mapped into parametric u v coordinates with u 1 on the axis u 1 on the waterline and v increasing from 1 to 1 as one moves along the waterline 1The cumulative length is defined here as the length of the vector sum of the waterline segments 10 5 in the positive direction counterclockwise when viewed from above the free surface The configuration paramet
448. wave elevation and or fluid velocity vector will be evaluated Here I 1 2 3 correspond to the X Y Z coordinates If Z 0 the resulting output should be interpreted as the nondimensional wave elevation 4 16 otherwise as the nondimensional pressure If NFIELD 0 no input should be made for the array XFIELD Additional data is required to specify the field point array XFIELD when field points are placed inside internal tanks as explained in Sections 4 7 and 12 1 When a large number of uniformly spaced field points are required it is convenient to use the alternative inputs described in Section 4 11 Starting in Version 7 1 the parameter TOLFPTWL is used to control the identification of field points on the free surface which are close to or inside body waterlines If one or more field points on the free surface are inside a closed waterline or within a nondimen sional distance of the waterline which is less than TOLFPTWL these points are identified as interior field points and the outputs for the hydrodynamic pressure and velocity are set equal to zero In the supplementary output file fre fpt the output O is appended on the line after the field point coordinates see Section 5 2 An example of this output is included in Test05a If TOLFPTWL lt 0 0 is input in the cfg files the test of free surface field points is skipped When TOLFPTWL is used to test the locations of interior field points only closed waterlines with nonzero thickness
449. with the higher order ILOWHICSF 1 subroutine ELLIPSOID CS in the GEOMXACT DLL library The corresponding output for the mean drift force and moment is contained in the file TEST05 9c It should be noted that the higher order control surface for the spheroid does not include the intermediate free surface patch and thus the horizontal drift force is correct whereas the vertical drift force is not complete The reason for omitting the free surface patch here is that the low order solution for the body does not give a sufficiently robust evaluation of field velocities and wave elevations at points on the free surface that are very close to the body The low order control surface is more suitable for use with low order body representations in this respect provided the panels on the free surface have dimensions similar to the dimensions of the adjacent panels on the body In Test05a the relative orientations of the two bodies are the same but they are po sitioned such that the 90 degree rotation of the spheroid is not required and the plane X 0 is a plane of symmetry for both bodies as explained in Section 8 5 This reduces the number of equations NEQN by a factor of one half and reduces the run time and storage requirements The outputs from the two runs are essentially the same except that the directions of the coordinates are changed with corresponding changes in the defini tions of the force coefficients and field velocities A rectangular arr
450. wn B spline coefficients NLHS Number of components to be solved when the total solution is decomposed into symmetry and antisymmetry components for the body having geometric symmetry NDFR The total number of degrees of freedom It equal to the sum of the degrees of freedom of each body NBODY Total number of bodies XBODY Normalized coordinates of the origin of body coordinate system and its orien tation relative to the global coordinates system XBCS XBCS 1 I and XBCS 2 1 are cosine and sine of XBODY 4 1 IBPTH L Body index for patch index L IBMOD N Global modes counter Number of modes prior to the present body N IGEO Parameter used to determine the sign of the pressure velocity on the reflected patches see MODE F ILHS Pointer of the given LHS among NLHS components IFLAT Index for patches on the free surface IFLAT 1 patches on interior free surface IFLAT 1 patches for flat physical surface on the free surface IFLAT 0 patches not on the free surface KU KV NU NV Orders and panels NMDS For given LHS total number of modes of radiation problem 5 7 MDS For given LHS MDS stores NMDS modes indices ICOL The solution such as motion amplitude is stored in the order which is not ascending from mode 1 surge ICOL stores the pointer in that sequence for all modes BETA Wave headings PER WVNFIN WVNINF IFREQ Period finite depth wavenumber infinite depth wavenumber IFREQ 0 normal
451. x OPTN 6vy OPTN 6vz If Option 6 is specified the supplementary output file frc fpt is created with the following format OPTN fpt L XFIELD L YFIELD L ZFIELD L If a field point is located on the free surface inside or on the waterline of a body a zero is added after the coordinates as explained in Section 4 3 and the format of the supplementary output file frc fpt is as follows OPTN fpt L XFIELD L YFIELD L ZFIELD L 0 Except as noted below the definitions of parameters in these files are as follows I J Mode indices M Index for quadrant 2 planes of symmetry or half 1 plane of symmetry If no planes of symmetry are specified or if IPNLBPT gt 0 then M 1 K Index for panels on the body surface L Index for field points PER Period BETA Wave heading BETA BETA Two wave headings for the mean drift forces and moments XCT YCT ZCT Dimensional global coordinates of panel centroid AREA Dimensional value of the area of a panel 5 3 Nz Ny Nz Components of the unit vector normal to K th panel in local coordinate system r x n x n y x n Components of the cross product of the position vector to the centroid of the K th panel and it s normal vector in the local coordinate system Here r is given in dimensional units XFIELD YFIELD ZFIELD Dimensional global coordinates of the field point In Option 5 when IPNLBPT 0 the index M refers to the body index and K refers to the body po
452. xciting moment about the y axis of Body 3 The phases of the forces and motion amplitudes and of the field quantities such as the field pressure and field velocity are defined relative to the phase of the incident wave at the origin of the global coordinate system The pressure drift force and moment Option 9 returns values for each body in its respective body coordinate system When Option 8 is specified momentum drift force and moment the quantities calcu lated are the global horizontal drift forces and mean yaw moment acting on the entire ensemble of bodies It is possible to compare these outputs with the total drift force and moment from pressure integration by summing the latter outputs for the forces and mo ments on each body This provides a useful check on consistency Special attention is required if the body coordinates are not parallel to the global coordinates system Chapter 9 GENERALIZED BODY MODES NEWMDS gt 0 WAMIT includes the capability to analyze generalized modes of body motion which extend beyond the normal six degrees of rigid body translation and rotation These generalized modes can be defined by the user to describe structural deformations motions of hinged bodies and a variety of other modes of motion which can be represented by specified distributions of normal velocity on the body surface To simplify the discussion it will be assumed that only one body is analyzed i e NBODY 1 The analysis of multiple b
453. xecute the hydrodynamic analysis for NBETA wave angles as explained below x XBODY 4 SH Sg XBODY 2 Figure 4 1 Sketch defining the global coordinates X Y Z body coordinates a y z and wave heading angle 8 The vertical Z and z axes are positive upwards with Z 0 the plane of the undisturbed free surface The origin of the body coordinate system is at the point X XBODY 1 Y XBODY 2 Z XBODY 3 A separate set of body coordinates is defined for each body if NBODY gt 1 BETA is the array of wave heading angles in degrees The wave heading is defined as the angle between the positive z axis of the global coordinate system and the direction in which the waves propagate as shown in Figure 4 1 The sign of the wave heading is defined by applying the right hand rule to the body fixed system In POTEN the wave headings specified in the Potential Control File pertain to the solution of the diffraction problem only If IDIFF 1 NBETA should be set equal to O and no data BETA should be included in the POT file If NBETA lt 0 a special convention is followed to assign a total of NBETA wave angles with uniform increments starting with the value equal to BETA 1 and using the increment equal to the value shown for BETA 2 In this case only two values BETA 1 BETA 2 should be included in the POT file This option is convenient when a large number of uniformly spaced inputs are required The two following examples show equiv
454. xplained in Section 4 7 Since waterline segments with a nondimensional length less than TOL are neglected it is possible for this error message to be output even when the actual gap is less than TOL due to the simultaneous occurrence of one or more gaps and or small panels More specifically the error message is output when the cumulative length of successive small waterline segments is larger than the prescribed tolerance for the gap When this error message is encountered the user is advised to re discretize the body surface to avoid panels with very small waterline segments and or large gaps between adjacent panels or alternatively to use the IRR 1 option which requires the user to dis cretize the free surface It is also possible to overcome this problem on an ad hoc basis by modifying the parameter TOLGAPWL Modification of this parameter is potentially dangerous if there are relatively short waterline segments The parameter SCALEH is defined in WAMIT with the value 1 4 This parameter is used when IRR 3 and ISOR 0 to set the typical length ratio between the sides of the triangular panels on the free surface and the side of body panels 10 4 AUTOMATIC FREE SURFACE DISCRETIZATION IRR 3 and ILOWHI 1 WAMIT includes the option to define the interior free surface automatically when the higher order method is used ILOWHI 1 This option can be used for multiple bodies for bodies with trimmed waterlines and for bodies with multiple
455. y be used to simplify this command 1 add c wamitv7 to the system PATH or to the system PATH when executing the installed wamit bat file or 2 use the batch file runwamit bat which is supplied in the testruns subdirectory 2 4 RUNNING TESTO1 Test run 01 evaluates the added mass and damping coefficients exciting forces motions wave elevations field pressures fluid velocities and drift forces for a freely floating trun cated vertical circular cylinder of radius 1 0m and draft 0 5m in infinite water depth for three wave periods and one wave heading angle Further details are contained in Section A 1 in Appendix A The corresponding input files test01 gdf test01 cfg test01 pot and test01 frc are included in the subdirectory c wamitv7 testruns In order to specify the appropriate filenames during the run first copy the file test01 wam to the file fnames wam Copying is recommended in preference to renaming the file to preserve the original file The appropriate DOS command is copy testOl wam fnames wam Next execute WAMIT This can be done by entering wamit if the WAMIT install direc tory has been added to your path Otherwise runwamit test01 will execute the provided runwamit bat file for test01 This batch file will remove old files associated with test01 copy test0l wam to fnames wam and execute WAMIT in one step During execution of the subprogram POTEN the monitor displays the starting time and after the solutions for the
456. y by POTEN or FORCE whereas other input files are used by both In this User Manual the font fnames wam indicates a specific filename and extension usually in lower case letters Upper case letters such as GDF are used more generally to abbreviate the type of file Filenames in italics e g pot p2f and frc out refer to the user defined filenames of the POT and FRC files from which the output files derive their own filenames 4 1 The following table lists all of the input files which may be prepared by the user and indicates the relevant subprogram s Filename Usage pot pot POTEN gdf gdf POTEN Freire FORCE gdf spl POTEN fnames wam POTEN FORCE break wam POTEN config wam POTEN FORCE cfg POTEN FORCE gdf ms2 POTEN gdf csf FORCE gdf bpi FORCE fre rao FORCE Description Potential Control File Sections 4 2 Geometric Data File Chapters 6 7 Force Control File Sections 4 3 4 Spline Control File Section 7 11 Filenames list Section 4 8 Optional file for runtime breakpoints Section 4 12 Configuration file Section 4 7 Configuration file Section 4 7 MultiSurf geometry file Section 7 7 Control surface geometry file Section 11 1 Specified points for body pressure Section 4 6 External RAO file Section 4 13 The first three input files are required in all cases The others are required in some cases or are optional as explained below The following table lists the output files which are prod
457. y large number of small panels may be required to achieve accurate results The second approach is to reduce the thickness to zero and represent the corresponding elements of the body by special dipole panels This approach is analogous to the thin wing approximation in lifting surface theory 21 WAMIT permits the user to specify a set of dipole panels as described in Section 6 3 This option facilitates the analysis of bodies with damper plates strakes and similar thin elements without the need to use very large numbers panels or to artificially increase the thickness 6 1 THE GEOMETRIC DATA FILE In the low order method the wetted surface of a body is represented by an ensemble of connected four sided facets or panels The Geometric Data File contains a description of this discretized surface including the body length scale gravity symmetry indices the total number of panels specified and for each panel the Cartesian coordinates x y z of its four vertices A panel degenerates to a triangle when the coordinates of two vertices coincide The order in which the panels are defined in the file is unimportant but each panel must be described completely by a set of 12 real numbers three Cartesian coordinates for each vertex which are listed consecutively with a line break between the last vertex of each panel and the first vertex of the next The value of gravity serves to define the units of length which apply to the body length scale
458. y near a wall In TEST19 IGDEF 0 is used with four patches specified in the GDF file corresponding to one quadrant of the catamaran configuration Since there are two hulls in this case the forces acting on both hulls are two times the corresponding forces in TEST04 but since the incident wave amplitude in TEST04 is increased by a factor of two the exciting force coefficients and RAO s are the same in both test runs except for small differences in accuracy Note that in TEST19 two planes of symmetry can be utilized unlike TEST04 where reflection about the plane x 0 is required by the program The comparisons of cross coupling coefficients and Haskind Diffraction exciting forces implies that the results of TEST19 are more accurate with less computational cost Generalized modes can be used to extend the analysis of this configuration to include two independent bodies In this case each of the rigid body modes of the catamaran must be supplemented by a corresponding generalized mode which has the same normal velocity on one barge and the opposite phase on the other The separate modes of each independent body are then evaluated by combining the corresponding symmetric and antisymmetric modes for the catamaran It is simpler to use the option NBODY 2 for this purpose but the number of unknowns is increased by a factor of four resulting in a substantial increase of the run time For the more efficient approach used in TEST19 it is necessary to rep
459. y pressure velocity data NPFORCE 1 4 integrate pressure forces only on panels patches 1 to 4 NPDIPOLE 2 4 6 dipole panels patches NPNOFORCE 1 4 do not include pressure on panels patches 1 to 4 NPTANK 8 11 12 15 range of panels patches on two internal tanks NPFSP 22 24 range of panels patches on FSP surfaces NUMHDR 1 write headers to numeric output files NUMNAM 1 Numeric filenames are assigned as OPTN PANEL SIZE 0 1 automatic subdivision of patches in higher order method RAMGBMAX 1 5 Gigabytes of RAM available for scratch memory RHOTANK 0 6 1 0 relative fluid densities in the two tanks SCRATCH_PATH d temp use temp directory on drive D for scratch files TOLGAPWL 0 01 tolerance for waterline gaps TOLFPTWL 0 do not check for field points on or inside body waterlines USERID_PATH c wamitv7 directory where userid wam is stored VMAXOPT9 10 0 output points on the body where the fluid velocity gt 10 XTRIM 1 2 0 Trim 1 unit vertically and 2 degrees pitch angle ZTANKFS 1 2 Elevations of tank free surfaces above the plane Z 0 4 88 FILENAMES LIST FNAMES WAM An optional input file may be used to specify the filenames of the primary input files POT FRC and GDF Use of this optional file is recommended The optional file must be named fnames wam This file includes a list of the input filenames above including their respective extensions cfg pot and fre
460. y sin p 15 4 Ww cosh kH where the wavenumber k is the real root of the dispersion relation 2 ktanh kH 15 5 g and 5 is the angle between the direction of propagation of the incident wave and the positive x axis as defined in Figure 4 1 In the limiting case of infinite depth k K To distinguish these two parameters they are referred to as the finite depth and infinite depth wavenumbers respectively The wavelength is equal to 27 k and the wave period is equal to 27 w The linearization of the problem permits the decomposition of the velocity potential y into the radiation and diffraction components P PR T YD 15 6 6 pr WD Ep 15 7 j l PD Po Ys 15 8 The constants denote the complex amplitudes of the body oscillatory motion in its six rigid body degrees of freedom and y the corresponding unit amplitude radiation poten tials The velocity potential ys represents the scattered disturbance of the incident wave by the body fixed at its undisturbed position We will refer to the sum 15 8 as the diffraction potential yp On the undisturbed position of the body boundary the radiation and diffraction poten tials are subject to the conditions Pin Nj 15 9 where n1 n2 ng n and n4 n5 nge X X n X x y z The unit vector n is normal to the body boundary and points out of the fluid domain The radiation condition of outgoing waves in the far field is applied to t

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