3D Mesh Generator Manual - The National Center for Computational
Contents
1. a Click button J 5 Stretch Function group In this group the stretching function parameters are set Stretching 3 Et Contract No far ep lo gt rr rr b Click button Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 24 Stretching Stretching 3 Contract No fi P 1 0 fo js E Iv Manually No of J Lines 10 c Check Manually d Click button Contract Pattern of nodal distribution according to current P D S Fig 3 13 Stretch Function Group This 1s the most complicated group It provides three main functions set the stretching parameters in each sub sections set the stretching parameters for I lines in the transverse direction and set the contraction or repulsion points along I lines When the user click the options and the check box the related inputting boxes will turn to same color as shown in Fig 3 13 e Bnd means Boundary lines of each subsection e means Mesh I lines e Manual distribution means Distribute mesh lines for each subsection manually e N LL means No of mesh J Lines distributed in the selected subsection N C P means of Contraction or repulsion Points L C P means Label of each Contraction or repulsion Point R L C P means Relative Loca2. 31 Las d Fig 2 6 Interior nodes Step 4 Interpolate the bed elevation discussed in detail later 2 2 Modified Poisson Equation The partial differential equation commonly used for the numerical mesh generation 15 the Poisson equation in the form of 0 n P n t Ox 6 7 zo Qu 2 4 y where 6 7 is computational coordinated system and x y is physical coordinated system P Q are control functions for the clustering of points Fig 2 7 Physical domain and computational domain Transforming the above equation 2 4 we obtain Chapter 2 Mesh Generation CCHE Mesh Generator 8 O x B PAS OM y _ Q y Q y where 2 8 61 0 8 _ x y y up 2 5b Y x y The orthogonal condition is g 0 2 6 Define P and Q in the following formulae 1 1 1 P Ev Q m 2 7 where gi h g 2 7b h x y o 2 7c h y gt x e y Qty P Yea Je m 7 2 d 2 7d yr A y x7 5 1 Cs Deus Vaan Ce 2 7 7 7 Using centered difference scheme to discretize equation 2 5 we obtain Chapter 2 Mesh Generation CCHE Mesh Generator 9 x Li 2X T3 JPY Gua 2X 0 50 P x E j_ d
3. eee 54 9334 HOW o Eal MSIE osea eas ab Re 55 SC NM Edl ITI LT 55 3 4 2 Adjust Mesh Node s or Line s Location eee eene 56 3 4 3 Modify the Properties of Mesh Node eee eee nenne 57 3 5 View Mesh In Different Ways eee eee enne nnne 56 3 5 1 View Bed Topography oeste ousue s orsoto edis e Ro RR OR Ue IDEE 58 3 5 2 View Bed Topography with Mesh on eee eere 59 RR VICW ID MICS T 60 352 VACW aE e aa ed ERROR SM E OUI EEG DI 61 PII E A I KDSDd EE 62 3 3 6 Add Baekor nd Pc 64 3 0 System RequiremteHs eres Se 66 3 7 Review of Formats of Files winston QUE DURS 66 3 7 Mesh Boundary File mesh bnd eee 66 3 7 2 The bathymetry Database File mesh xyz 66 3 7 3 The Measured Cross Section File mcs 69 3 7 4 The Mesh Geo BED 70 Conclusions cce eeeeeeeeeoeoooosoccecceceeceececceceeces L References Chapter 2 Introduction CCHE Mesh Generator 1 Chapter 1 Introduction The mathematical modeling of hydrodynamics and sediment and pollutant transport involves a set of partial differential equations Navie
4. MS SS a Original database b refined database Fig 3 42 Original database and refined database If the bed bathymetry database file 15 ready click Bed and choose Interpolate Random and then the interpolation begins Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 53 Open Bed Geometry File TET a bend_low mesh_xyz Cor SES Suter E My Netwark File bend mesh Files of type mesh_xyz File mesh xyz Cancel Open as read only Fig 3 43 Open the Geometry File Step 7 Save the mesh as geo file So far the algebraic mesh 15 completed If the mesh 15 satisfactory the user can save the mesh as geo file which is to be used by CCHE2D and CCHE3D model 3 2 5 Generate Near Orthogonal Adaptive Mesh CCHE2D Mesh Generator solves the modified Poisson Equation to generate near orthogonal adaptive mesh The three non negative parameters orthogonality smoothness and adaptivity need to be evaluated before computing Among these three parameters the orthogonality and smoothness whose sum 15 one are dependent upon each other and they are both less than one and the adaptivity 1s independent parameter Note if the option Keep the measured cross section 15 checked those sections will be fixed during the generation This option 15 available for both the numerical methods and the smoothing methods Chapter 3 Inteface of CCHE
5. Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 38 Fig 3 25 Specify the control points for block 3 Step 6 Click Save and save all the information as a boundary file 3 2 2 Generate Mesh from Topographic Image If the topographic image 15 available the user can generate mesh directly from it The procedure is almost the same as the previous section Step 1 Click Topography menu and choose Load Topographic Image Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 39 Look in Sa 0607 2002 Fav History Desktop Documents Computer Files of type Bitmaps bmp Cancel Open as read only File name 037089F5 bmp 2 Smoohaess o gt r Keep Measured X Bechons Local Smoothing Mesh X Section Stretching at cona fe Pp op zi F Mami No oiua gt 4 9 Mesh Generator v2 1 x 3100 323003 2766 426502 Fig 3 26 Load the Topographic Image Step 2 Click Boundary button in Edit group and create the boundary with the help of Edit Boundary window Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 40 D Je E m fie pm db S zu lA enl ELITS Br oe d ill Fig 3 27 Create Boundary Step 3 Transform the local coordinates sy
6. x x N P 2 17 k l N B y N B 2 17b where is the number of nodes around P the superscript n means the new value Note that the number of nodes around P is dependent on the shape of the element For the quadrilateral elements the number of nodes around 15 always 8 Fig 2 8 Chapter 2 Mesh Generation CCHE Mesh Generator 14 Fig 2 8 Laplacian 8 points polygon averaged method smoothing method is often applied with several iterations Under relaxation is used to avoid abrupt change of the nodal location which could also reduce the mesh distortion near the boundaries caused by smoothing x l w x 2 18a w y tw y 2 18b Where 0 lt lt 1 2 5 Interpolation of Bed Elevation Given the basic bathymetry data there are several methods available for interpolating bed elevation from a database to the mesh points such as Taylor series expansion method Lagrange interpolation method inverse distance interpolation method etc Chapter 2 Mesh Generation CCHE Mesh Generator 15 Random Database For non structured bathymetry database an inverse distance method is often used in CCHE mesh generator which requires selecting four surrounding points to complete the interpolation The procedure to search these surrounding points is shown Fig 2 9 First mesh point is placed at the origin of a local Cartesians coordinate system In each quadrant a p
7. Boundary Creator Black 1 ft Block fi v BeckType fi f Top Boundary Bottom Boundary Untrictured Bnd Connect Nodal Type Normal Bnd Add Island Island No X 7501 250t 16214 238147 Location zum Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 34 Fig 3 21 Specify control points on top boundary of the first block 6 Choose option Bottom Boundary and apply the similar operations Note that the number of control points on the bottom boundary must be equal to the number of points on top boundary m lal es Boundary Creator Block I Top Boundary Bottom Boundary _ Uniructured BF connec Nodal Type Normal Bnd Add Island Island No x 8208 4782 Y 14801 1830081 Location Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 35 Fig 3 22 Specify control points on bottom boundary of the first block 7 Make sure all the parameters of the first block specified and then move onto the next block Step 4 Specify the control points for the second block and note an island 15 required to added into this block 1 Evaluate the block 1 J values as 2 1 and then do the same operations as block 1 Boundary Creator Block 3 i lt TepBoundary c Bottom Boundary _ Unwcwred Bd Nodal Type Normal Bnd Add
8. Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 22 Evaluation Report Smoothness Orthgonality otal Fig 3 8 Evaluation report window Click Display Labels of Control Points and the control sections will be marked Fig 3 9 Display Labels of Control Points Click Edit Properties of Mesh Nodes button an edit pen window will pop out and the user can modify the local information of the mesh Details will be covered in later section Edit Pen Properties ol x Edit Pen Properties E X Coordinate fo Single Point C Multi Points I No of First Node 85 I No of Last Node 85 Y Coordinate NN 2 Coordinate iv 2 7 Manning s n fo Undo OK J No of First Node 24 J No of Last Node 24 Undo Cancel OK Fig 3 10 Edit pen window Chapter 3 Inteface of Mesh Generator e Mesh Editing Add J Line Move Node Edit CCHE Mesh Generator 23 Add I Line A Je IL mu Delete J Line Save Changes Undo Previous Change Delete I Line Fig 3 11 Tools for Mesh Editing e Mesh Viewing Zoom Out Pan Zoom In X Restore Locator Increase Z Decrease Z Fig 3 12 Tools for Mesh Viewing Stretching 3 Contract fan Dh op Manually No of J Lines 0 ere SS
9. means right side i d of side 2 1 means wall bnd and 0 means no bnd i d of four bnds of four sections 3 2 4 Generate Algebraic Mesh Using the data of Tab 3 1 as boundary file now the user can generate the mesh step by step Step 1 Input the boundary file Click File menu and choose Open Bnd File Open Boundary File bow mesh bnd za aaa TES Nu us My WES are sje File name bs l testmaesh bnd Files of type mesh bnd File mesh bnd Cancel Openasread anly 2 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 45 Fig 3 32 Open Boundary File Step 2 Generate the mesh for block 2 Because block 2 has a dike it is recommended to begin with this block For the domain with a dike the user always cares more about the area near the dike On each side of dike and around the tip the mesh should be denser For this special consideration stretching function 1s needed to generate the non uniform mesh First evaluate the mesh size x Jna 93 x 45 and then generate the mesh using the default parameter values However the mesh 15 nearly uniform which 15 undesired Fig 3 32 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 46 Fig 3 33 Uniform Mesh for Block 2 Now go to the Stretch Function group and adjust parameters Block 2 has 6 pairs of control points which divide the block into 5 subsections The user needs to adjust the
10. lcs np k label and number of points of cross section DO 1 np k X y Z of each points Read 13 xcs k j yes k j zes k j ENDDO ENDDO 3 7 4 The Mesh Geo File geo The mesh geo file 15 an output file of CCHE mesh generator The format in Fortran code is as follows Open 14 file test geo Write 14 jmax imax maximum number of 1 lines and J lines DO 1 7 1 imax DO j 1 Write 14 xpQ J 284 J zpG J 1d 1 J rough ENDDO ENDDO Conclusions CCHE Mesh Generator 73 Conclusions The CCHE2D Mesh Generator and its GUI have been developed for generating algebraic and numerical computational structured meshes It provides quite a few effective methods to generate mesh with its quality guaranteed A flexible and powerful two direction stretching function 1s applied to generate algebraic mesh and both a Poisson equation based solver whose source terms are based on control functions and the variational approach with several optimal objectives controls are used to generate numerical mesh The Laplacian smoothing scheme is applied to smooth mesh A multi blocks idea is applied to generate mesh for the domains with complicated geometry GUI 15 also developed to make the mesh generation more efficiently and easily During the process of its development this generator has been applied to generate meshes for several computational simulation projects suc
11. the coefficients are reproduced from the cited paper and presented below d i 1 2 3 b Asbs 1 2 3 i 1 2 3 d Aa b a as Ay b where y R3 C 2x tx and A 2 2 _ t Ys og Tete 7 yp d a J 7 J 2 16c 2 16d 2 16e 2 16f Chapter 2 Mesh Generation CCHE Mesh Generator 13 2 2 dy Oy us i Xg Yes Dy 2 ye y Cy 2X X 2 16g 2 2 aw Xgyes Dy do X Y Do X jl bo 2 2x x Co 2 2 Do X Co 2 16 2 4 Laplacian Smoothing Method Because of way the algebraic mesh 15 generated the global properties of the mesh such as uniformity orthogonality could not be guaranteed to be optimal Smoothing method could be applied to further improve these generated meshes The Laplacian smoothing scheme is currently adopted in CCHE2D Mesh Generator This method can be applied locally to improve local nodal distribution and avoid massive global change The Laplcaian smoothing method is to move one interior node to the center of the polygon formed by the elements around this node For any internal node P y Laplacian polygon smoothing method 15 expressed by
12. 0 50 0 50 X ja 2 10a Q y n Mist pU EN Jia T C juo us del 0 50 0 50 T Via tr 1 T 2 10b T 0 c tcu tY atc 2 10c where r is the effect control factor and 0 lt r lt 1 and cj 15 the contribution factor Note that Equation 2 10 is the same as 2 9 when r land c 1 When generating adaptive mesh the contribution factor 1s evaluated by the following equation Z Z 2 11 2 zZ max min where 15 the adaptivity parameter and r gt 0 and z is bed elevation 2 3 Variational Laplace Equation The variational Laplace equation is adopted in this version of CCHE2D Mesh Generator Three indices could be used to evaluate the quality of a mesh system uniformity orthogonality and adaptivity Uniformity indicates the mesh spacing is uniform distributed Orthogonality is a measure of how much the mesh lines are perpendicular to each other and adaptivity is the nodal distribution to areas where higher resolution and accuracy are desired The adaptivity of the mesh is measured by the functional Chapter 2 Mesh Generation CCHE Mesh Generator 11 I w x y JdA 2 11 D where J XY Z 2 12 is the Jacobian which represents the area of a computational cell in 2 dimensions When this integral is minimized w x y J with w x y gt 0 should have a uniform distribution so that where
13. 2 8a 0 50 O X 5 0 20 a ty 2Y i 0 50 P Y ja Y ai T 2 8b 0 59 QCy Y Lia 0 where a 0 25 x op TO apes 2 8 0 25 x i X L4 y Y au 7 1 2 8b m X aX ua ES Y ua E X i E aX Vaal 16 2 8d Rearranging the equation 2 8 we obtain y 0 50 x x x x x P x jii 2a 2y 7 11 X it 20 2 7 1 1 jiu 20 2 3 1 X j 0 50 Xia Xe 2 9a 20 2 O fark 0 5 Vig 2 aat 20 2 0 50 0 2 9 2a 2y OV ii In order to generate 2D near orthogonal mesh with high smoothness and adaptivity we modified the conventional Poisson equation by introducing effect control factor and contribution factor The effect control factor combines the conformal mapping and the orthogonal mapping together which is capable of preventing mesh distortion and overlapping effectively and also enhancing the convergence of mesh computation due to the fact that Laplace equation 15 numerically more stable than Poisson equation With contribution factor adaptive mesh generation 1 depth adaptive mesh temperature adaptive mesh etc becomes possible Chapter 2 Mesh Generation CCHE Mesh Generator 10 The modified Poisson Equation reads y xij T ny Xu m
14. Connect button and all the generated meshes are linked into one big mesh Blocks Block 1 Connect Imax 150 Imax 130 Fig 3 2 Block Group 2 Generate group Generate Algebraic Poisson Laplace Laplacian Iteration 10 1 0 smoothness 1 0 Adaptivity 1 Keep Measured X section Local Smoothing Fig3 3 Generate Group This group is a collection of commands to generate a mesh including six command buttons four inputting boxes and two check boxes Once a command button 15 clicked an Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 19 action of the mesh generation 1s activated and this button will turn into yellow to provide a friendly reminder Click Algebraic button and the algebraic mesh will be obtained Usually this is the first button one needs to push when generating a mesh e Click Poisson button and the Poisson Equation for orthogonal mapping will be solved e Click Variational button the Variational Laplace Equation will be solved to obtain adaptive mesh e Click Laplacian button and the mesh will be smoothed using Laplacian polygon averaged method e Click Laplace button and the Laplace Equation for conformal mapping will be solved e Click Bed button to interpolate the bed elevation based on the survey database Details will be covered
15. EM se 0 Manually oid Lines 6 64 4 t Move leftward b Move rightward Taone Poisson 1 YWorintional IE Smoothness Palepiliviby fio Koop Local Smoothing 4 a 1 gt op xs zi Manually 15 2639 MET Move upward Fig 3 14 Control Panel T Local Smoothing Connect imax 10 Generis erate Poisson apada eration Koop Measured X Sechinns ss t d Move downward Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 26 3 1 3 Menus There are three menus in the main window File menu View menu and Bed Elevation menu File menu provides the operation of the files while View menu provides the view tools of the picture Bed Elevation menu provides functions related to bed elevation View Topography O Open Bnd File Save as Bnd File Open Geo Save Geo Save as Geo File i Open WorkSpace sace WorkSapce Save as WorkSpace amp bPrint amp Print Preview Save as Image File ms 7d mesh bnd view Topograpt di 2 55901 zoom In n bd zo
16. a first sub section b second sub section Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 57 c mesh Fig 3 46 Application of stretching function in I direction 3 3 2 Apply Stretching Function in J Direction Secondly the stretching function is applied in J direction As shown in Fig 3 43 in J direction there are three control points which divide the boundary into two sub sections The stretching function 15 applied to these two sub sections respectively As shown in Fig 3 46 first click option Bnd and check Manual Distribution in group of stretching function and then evaluate the parameters in blue color N J L represents the number of J lines specified in the selected sub section Stretching 3 Contract D fos I Manually No of J Lines 7 O Stretching 1 Contract No 1 fi 5 5 s 3 M Manually No of J Lines 7 first sub section b second sub section Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 58 c mesh Fig 3 47 Application of stretching function in J direction 3 4 How to Edit Mesh 3 4 1 Edit Boundary When a boundary file or a work space file or a Geo file 15 opened the user can edit the boundary if necessary This can be done by the following procedure 1 Click Boundary button of Edit group to activate this function You will find that bo
17. axis Two types Cross Section No and Distance are available Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 65 Cross Section in Horizontal Direction 4 4 4 4 Control e C J Multi Control ea C J Multi 5 X Me a1 X Axis CORSET H Fig 3 53 Different types of X axis Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 66 ae Gross Section in Horizontal Direction d Gross Section in Horizontal Direction View 905 1357 1810 Control Control J M Multi 2 Max 421 C J v Multi 5 30 33 36 42 X Axis v Inverse X Axis i Cross Section No Inverse lt Axis Fig 3 54 Multiple Cross Sections 3 5 6 Import Associated Topography When a boundary file or a work space file or a Geo file is opened and if the corresponding topography database 15 available the user can import the database as background The process is composed of two steps 1 Click Load Topographic Database and a question you want to import the associated geometry will be asked Choose Yes 2 Open the associated database file Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator
18. completed block If the block is not completed an error message will be given Boundary Creator 151 Block Und Block Type __ J C Top Boundary Bottom Boundary Untructured Bnd Mm Nodal Type End gt Addisland Island fi fa R exswz Y emrsmenes tcon save Fig 3 19 Click Island There are five inputting boxes and two options in this group and they are e Island records the number of islands in current block e Location 15 the relative location of the first pair of control points of the current island in current block Option Top Boundary means that the operation is worked on the top boundary of the current island Option Bottom Boundary means that the operation is worked on the bottom boundary of the current island No records the number of control points of the current island e X 15 the x coordinate of the control point of the current island Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 32 Y is y coordinate of the control point of the current island There are three command buttons in this boundary creator window Currently Connect is not enabled e Click Undo and the user can cancel the current action Click Save and the boundary file will be created and saved into a file In current version two new
19. has to be handled with a GUI to have high efficiency Based on these considerations CCHE2D Mesh Generator has been developed The current version not only has an interactive interface but also combines several methods for users to select Since the current NCCHE models use structured mesh this version of CCHE2D Mesh Generator only produces the structured mesh Both the sophisticated methods of solving partial differential equations and simple algebraic method are available The later is based on a flexible and powerful two direction stretching function and the former are a Poisson equation based solver whose source terms are based on control functions and the variational approach with several optimal objective controls To take advantage of the GUI a mesh can be generated by matching small mesh pieces together The GUI is newly developed for the CCHE2D Mesh Generator which is in the process of testing and further improving Users are encouraged to contact NCCHE if difficulties are encountered in generating a mesh Contents CCHE Mesh Generator Contents Title Page No Chaple IMEEM MEME ME PIECE e riu qe ha dp 2 VA ETT ITI RE M ZL A SUCICNING Funcion ee 3 2 1 2 Generation Steps cccccccccccsssssseseececcccccccnccsssececececccccanaesssess 5 22 POISSON E U
20. is relatively straight and it Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 43 may or may not be attached to the bank For the domain with some hydraulic structures not only the physical coordinates but also the relative ocation of the structures must be known In general Location means the global number of the control points of the structures For each of the hydraulic structures the format is different Tab 3 1 only shows the format of the islands The formats of straight dikes 15 shown in Tab 3 2 Tab 3 2 Format of Right Dikes No of straight Dikes No Location 1 Ydn 1 Xup 1 1 Xdn 2 Ydn 2 Xup 2 Yup 2 Note 1 The straight dike must have only two pairs of control points otherwise it will be treated as an island 2 Location here is the global number of the first pair of control points of the dike The compound dike 1s defined as the mixture dike consisting of two dikes with different angles as shown in Fig 3 31 Bank Flow Fig 3 31 Compound Dikes So there are three control points on each side of the dike and the river 15 divided into four sections in the transverse direction Tab 3 3 Format of Compound Dikes Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 44 No of Compound Dikes x2 i dofside i d of four bnds of four sections No Location 1 1 Xc 2 Yc 2 Xc 3 3 Note 1 1 means left side of dike and 1
21. m y coordinate of m th control point on bottom boundary of island n in block k xht k n m x coordinate of m th control point top boundary of island n in block k yht k n m y coordinate of m th control point top boundary of island n in block k compound dike mb_cd k number of compound dikes x 2 in block k id_cd k n type of compound dike n in block 1 left side 1 right side id_bnd k n 4 boundary type of four sections of compound dike n in block lid_cd k n relative location of compound dike n in block k xcd k n 3 x coordinate of three control points of compound dike block ycd k n 3 y coordinate of three control points of compound dike n in block k 3 7 2 The Geometry Database File mesh_xyz The geometry database file is used to interpolate bed elevation of mesh nodes The format of this file 15 very simple and the reading format in Fortran code 15 as follows Open 12 file test mesh xyz Read 12 nip number of points DO k 1 nip Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 72 Read 12 xip k yip k zip k x y z of each point ENDDO 3 7 3 The Measured Cross Section File mesh mcs The measured cross section data file 15 used to refine the original geometry database The format in Fortran code 15 as follows Open 13 file test mesh mcs Read 13 ncs number of cross sections DO k 1 ncs Read 13
22. out e Click Save as Image File and the picture drawn on the screen will be saved as a bitmap file e Click Skin and a submenu will be shown where there are two menus skin and Set Skin Set skin allows the user to choose a picture as the background for the main window and skin will clean the background ub02 jpg ujCandyRock pg WWAGauze3 jpg e Eb03 jpg amp Colors3 ipg amp iGroundla jpg 4604 amp iCracket jpg Hedge jpg 4 5 2 101 9 EECuItTextL jpg 1102 jpg HEIbO8 jpg Denim 1 jpg 103 jpg 1 3609 jpg 9 304 ER 10 9 amp llo5 My Documents steel jpg HiFence jpg HEII06 jpg amp Blueswir jpg EFlowers2 ipg 1107 jpg 1 HBump 1f jpg HFractal9 jpg 8108 irs My Computer gt 4 mt E Network Pla File name Files of type Graphic Files v Cancel Open read only 2 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 28 CCHESD Mesh Generator v2 0 21 Case WhiteBiver ut5 geo 89494 6 Black i Block 1 Connect e 227 Algebraic Prison Laplace Lnpacinn Vinsintianal d Heration Ovthaqonality Adaptivity 10 ia Keep Mpnnured Sections Lacal S
23. 67 ncche mesh Fig 3 55 Import the associated geometry Fig 3 56 Add a Background Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 68 3 6 System Requirements The current version of CCHE2D mesh generator is developed for Microsoft Windows 98 Windows NT Windows 2000 and Windows XP The users of other operating system should be careful that the mesh generator could not work or work incorrectly in those systems The resolution of 800x600 15 the minimum requirement for CCHE2D mesh generator and it s recommended to use higher resolution And the best resolution 15 1280 x 1024 3 7 Review of Formats of Files Used in CCHE Mesh Generator There are five files used in CCHE mesh generator the mesh boundary file mesh bnd the bathymetry database file mesh xyz the mesh work space file mesh wsp the measured cross section file mesh mcs and the output mesh file for CCHE2D and CCHE3D models geo The user needs to be familiar with the formats of these files except the mesh work space file The formats of these files in Fortran are reviewed in detail as follows for convenient reference 3 7 1 The Mesh Boundary File mesh bnd The format of mesh bnd file 15 a little complex The reading format of this file in Fortran code is as follows Open 11 file test mesh bnd input global information Read 11 mb imax mb jmax mb npmax Chapter 3 Inteface of CCHE Mesh Generator CCHE Me
24. AOO C 7 2 3 Variational Formulation 9 2 4 Smoothing Methods e usucsus TP RO PETERS 11 2 5 Interpolation of Bed Elevation 14 gm 0 Interface of CCHE2D Mesh Generator 16 3 1 Introduction of Interface 16 3 1 1 Groups of Main Window aos suuesvsusuzezewe dus 17 25 DN RSS VICTIUS Er 26 3 2 How to Generate a Mesh 26 3 2 1 Generate Mesh from Topographic Database file 26 3 2 2 Generate Mesh from Topographic Image eere 35 3 2 3 Generate Mesh from Boundary File eee eee eee 36 3 2 4 Generate Algebraic Mesh ccce eee ecce eee eee eee eee neenon 40 3 2 5 Generate Near Orthogonal Adaptive Mesh eese 50 3 2 6 Generate Variational Adaptive Mesh ee eeee eee eee eene nne 51 Contents CCHE Mesh Generator Generate SINOOUL Mesh ERE PT cm 51 3 3 How to Use Stretching Function eee eee eee ee 51 3 3 1 Apply Stretching Function in J Direction eee 52 3 3 2 Apply Stretching Function in I Direction
25. Island Island No X 10439 61t 15024 296978 Location Gave Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 36 Botto m Fig 3 23 Specify the control points for block 2 2 After this block is completed click Add Island Choose Top Boundary and then do the same operations as block to specify the control points of top boundary of the island 3 Choose Bottom Boundary to specify the control points of bottom boundary of the island 4 Evaluate the Location as 3 Boundary Creator Block Und 2 Block 2 Block End Unde J C Boundary Bottom Boundary Untructured Bnd Connect Nodal Type Normal Bnd Addisland Island f No 2 9714 4977 Y 15600 674731 Location 3 Gave Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 37 Fig 3 24 Add island into block 2 Step 5 Specify the control points for the third block First click Structured Bnd to switch from island operation to block operation Evaluate the block I J values as 3 1 and then do the same operations as block 1 Boundary Creator 15151 Black f Block v BeckType gt _ StructuredBnd Unde J Boundary Bottom Boundary Untructured End Ta Normal Bnd Add Island Island 1
26. Mesh Generator CCHE Mesh Generator 54 3 2 6 Generate Variational Adaptive Mesh CCHE2D mesh generator solves the Variational Laplace Equation to obtain the variational adaptive mesh Similarly the three non negative parameters orthogonality smoothness and adaptivity need to be evaluated before computing However in this approach these three parameters are all independent upon each other 3 2 7 Generate Smooth Mesh There are two methods available to generate smooth mesh one is through solving Laplace Equation for conformal mapping and the other is through the Laplacian smoothing scheme Check the option Local Smoothing the user can specify the smoothing area by choosing two mesh nodes which are the diagonal points of the quadrilateral area specified for local smoothing otherwise the whole domain will be smoothed 3 3 How to Use Stretching Function The stretching function is often used to distribute nodes along the boundaries In CCHE2D mesh generator the stretching function can be applied in two directions J and I Note that at each time the stretching function can be applied to only one line or sub section Here an example 15 presented to illustrate how to use the stretching function to control the mesh density As shown in Fig 3 43 the mesh size in a rectangular domain 15 35x35 and it 1s required that 1 repulsion occurs at the node A B C and D 2 contraction occurs at the line EF and GH CCHE Mesh Generato
27. National Center for Computational Hydroscience and Engineering CCHE2D Mesh Generator and User s Manual v 2 00 Technical Report No NCCHE TR 2002 5 November 2002 Yaoxin Zhang and Yafei Jia CCHEZD Mech Gomorntor v2 0 x 2 4 0 4677262 0 68 School of Engineering The University of Mississippi University MS 38677 CCHE2D Mesh Generator and User s Manual Version 2 0 NCCHE TR 2002 5 Project Director and Principle Investigator sam S Y Wang Ph D F A P Barnard Distinguished Professor and Director Center for Computational Hydroscience of Engineering The University of Mississippi University MS 38677 Senior Investigator Yafei Jia Ph D Research Associate Professor Center for Computational Hydroscience of Engineering The University of Mississippi University MS 38677 November 2002 Abstract CCHE Mesh Generator Abstract This documentation describes the methodology and the Graphic Users Interface of a mesh generator CCHE2D Mesh Generator Mesh generation for computational hydrodynamic problems 15 usually a complicated and time consuming task which often discretise the irregular geometry of river channels reservoirs to a system of finite sized elements on which the numerical simulations are carried out Because of this one has to combine and utilize a collection of methods for different mesh generation needs and these methods and their tedious manipulation
28. Yafei Jia Senior Investigator of NCCHE Mr Yaoxin Zhang a Ph D student of NCCHE is in charge of implementation Chapter 2 Mesh Generation CCHE Mesh Generator 2 Chapter 2 Mesh Generation There are two main types of meshes used in numerical calculation structured and unstructured The structured meshes consist of families of mesh lines with the property that members of a single family do not cross each other and cross each member of the other families only once There are two kinds of methods to generate structured meshes numerical methods and algebraic methods The numerical methods solve the partial differential equations usually Poisson equations to generate boundary fitted mesh while the algebraic methods determine the mesh directly according to some desired nodal distribution The numerical methods are global approaches which can provide very good meshes with smooth transition of nodal distribution smoothness and orthogonality guaranteed Although the algebraic method can always be used to resolve a mesh its global smoothness even local smoothness uniformity properties are not guaranteed As a result smoothing methods are often applied to optimize the mesh For cases with complicated domain geometry the multi block approach could be applied to simplify a complex mesh to several small meshes with simpler geometry In practice the algebraic method numerical method and multi block method are used in combinatio
29. anges are stored only into the memory not the file 3 4 3 Modify the Properties of Mesh Nodes Sometimes the user may want to evaluate or modify the properties of the mesh nodes which are X Y Z coordinates nodal I D and Manning s n Click Edit button in Mesh Information group a edit pen window will pop out There are two pages of this window and the user can push gt gt or lt lt button to switch between them Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 60 Coordinate 0 Y Coordinate 0 of First Node of Last Node Coordinate 0 J of First Node Manning s n J Mo of Last Node Fig 3 48 Edit pen window In the first page there are five check boxes and five inputting boxes which represent the five properties of the mesh nodes Check one box and the corresponding inputting box will turn yellow Click OK and the values of the checked inputting boxes will be stored into the edit pen Click Cancel and the values stored in the edit pen will be cleared In the second page there are two options and four inputting boxes The user can either choose Single Point to evaluate or modify the properties of one specified mesh node using the values stored in the edit pen or choose Multiple Points to evaluate or modify the properties of the multiple specified mesh nodes So there are two ways to modify the properti
30. atabase will begin Click Interpolate Structured and the bed interpolation based on the structured survey database will begin Click Refine Database and the structured survey database will be refined Click Elementate Database and the structured survey database will be discretized into elements triangles and quadrilaterals Click Smooth and the user can smooth the bed elevation of the specified area How to Generate a Mesh 3 2 1 Generate Mesh from Topographic Database File At the beginning topographic database 15 the only file available This database file can be used not only as the interpolation database but also to create a boundary file required for mesh generation An example will be shown how to make a boundary file using geometry database file Note the geometry database file has the extension mesh Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 30 Boundary Creator The boundary creator plays an important role during this process and it will be introduced in detail as follows Boundary Creator Black C Top Boundary Bottom Boundary __Untructured Bnd leno E l x E ME n Modal Type Normal Bnd Add Island Island No 1 x Y Location Fig 3 18 Boundary Creator Window In this window there are three groups Structured Bnd group Unstructured Bnd group and I
31. ctively Fig 2 1 Chapter 2 Mesh Generation CCHE Mesh Generator 4 Fig 2 1 b lt 1 one direction stretching function In this version of CCHE mesh generator an improved more flexible and powerful two direction stretching function 1s used 7 1 2 1 2 C 2 24 LG te 26 n D xs 2 2b n where 5 is the relative location j is the label of nodal points n is the total number of points P 1 0 1 1s the exponential coefficient called Power parameter It determines if the points will be contracted or repulsed or uniformly distributed D 15 the deviational coefficient 0 lt D lt 1 called Deviation parameter It determines the relative location where the points will be contracted or repulsed S is the parameter used to control stretching degree called Scale parameter It determines in what degree the points will be contracted or repulsed The effects of P and D are shown in the Fig 2 2 In the following figure the location of any node along this line AB 15 calculated by 8 2 3 Chapter 2 Mesh Generation CCHE Mesh Generator 5 Two direction stretching function mmm 0 25 P 1 0 mmm 0 5 P 1 0 D20 75 P 1 0 c D 20 5 P 0 25 P 1 0 mmmE 0 5 P 1 0 mmmm 0 75 P 1 0 Fig 2 2 The Effects of P and D 2 1 2 Procedures to Generate Algebraic Mesh It has been mentioned that a mesh for a computatio
32. e interpolation due to surrounding available survey points 15 applied As for the structured survey data such as those measured section by section along a channel a refined database method due to thalweg 15 applied The file with the extension mesh mcs is identified as the measured cross section data file which 1s used to refine the original database The format of this file is shown in Tab 3 7 Tab 3 7 Format of mesh mcs file No of Total Cross Section Index of Cross Section No of Points on the Cross Section If the structured measured cross section data 1s available the user can choose the refined database method to improve the accuracy of the interpolation Click Topography menu and choose Refine Database the refinement process will begin At the end of this process the refined database will be saved Bedblevation Interpolate Randami Interpolate Stridctured Refine Database Elereritate Database smooth Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 52 Open Measured Cross Section Data Lookin C han94 database 6 Fav History 144 Type MESH MCS Size 151 Desktop My Documents uter e name han84 B mesh mcs Files of type Messured Cross Section Data file mesh mcs w Cancel Open as read only 2 Fig 3 41 Open a mesh mcs file
33. eds to do 15 to evaluate mesh size Laa XJ max and then click Algebraic button then the user can get an algebraic mesh max mesh generator can only identify the boundary file with an extension mesh bnd The format of this boundary file is shown in Tab 3 1 Tab 3 1 Format of Boundary File U 9 MaxINo ofBlocks J No of Blocks No of Control Points of Blocks Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 42 0 1 1 Four Bnds i d left downward right upward 1 wall bnd 0 not a bnd 3 27 40 59 56 2927 56 54 No Xdown Ydown Xup Yup 3 pair of control points 5 29 13 60 63 30 79 57 40 No Xdown Ydown Xup Yup 5 pair of control points No of Compound dikes x 2 0 0 1 0 1 Four Bnds i d left downward right upward 1 wall bnd 0 not a bnd 3 36 13 62 42 34 86 58 60 No Xdown Ydown Xup Yup 3 pair of control points 1 No of Islands 2 No of pairs of control points of island 0 1 0 1 Four Bnds i d left downward right upward 1 wall bnd 0 not a bnd 3 43 82 60 49 41 87 57 50 No Xdown Ydown Xup Yup 3 pair of control points 5 46 60 58 64 4463 55 74 No Xdown Ydown Xup Yup 5 pair of control points 6 48 10 57 51 45 88 5438 No Xdown Ydown Xup Yup 6 pair of control points CCHE mesh generator can identify three kinds of hydraulic structures straight dikes islands and compound dikes Straight means that dike
34. es of mesh nodes The default way 15 point by point When using this way the user doesn t need to go to the second page After clicking the user can modify the properties of the mesh node through the following operations Press Ctrl and hold it then use right button of the mouse to click the desired node If the user chooses Multiple Points he can use the four inputting boxes to specify range of the mesh nodes where the properties will be set or modified Click and then the properties of the mesh nodes in this specified range are changed Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 61 The user can use Undo to recover the changes of the previous step before Save Change 3 5 View Mesh in Different Ways After the interpolation of the bed elevation 1s finished the user can view the mesh in different ways by pushing the buttons in the Display groups 3 5 1 View Bed Topography Click Bed and the color shade picture of the bed topography will be shown Fig 3 49 Fig 3 49 Bed 3 5 2 View Bed Topography with Mesh on Click Grided Bed and color shading picture of the bed topography with grid will be shown Fig 3 50 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 62 Fig 3 50 Bed with Grid 3 5 3 View 3D Mesh Click 3D for the odd time and the 3D topography with mesh will be shown click it for the even ti
35. features are added into the boundary creator Reminder of top and bottom boundary in the first block two labels are provided to remind the user which boundary he 15 working on e Reminder of the directions of I and J of the blocks Now an example will be discussed in detail to demonstrate this process Step 1 Click Topography menu and choose Load Topographic Database File A bend channel is loaded and it will be divided into three blocks in which there is one island Open Bed Geometry File alx Look in E mesh E huang 654 sh xyz icon bs4n mesh_xyz liconz2text S 3ia khan _1 _ E D d Network Pla bend mesh oy E Files of type mesh xyz File mesh xyz Open read only 2 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 33 aw 7 Fig 3 20 Load Geometry Database File Step 2 Click button in Edit Tool group and the boundary creator will pop out Step 3 Specify the control points for the first block 1 Evaluate block I J values as 1 1 2 Choose option Boundary 3 Press Ctrl key and hold it 4 Move the mouse pointer to the desired location and press right button Thus one control point 18 specified 5 Repeat this process until all the control points on the top boundary are specified
36. h as the channel downstream of Wan An Reservoir with many dikes and an experimental channel with submerged weirs etc The experiences and the simulation results of CCHE2D and CCHE3D models have shown that CCHE mesh generator 15 capable of providing desired meshes for 2D and 3D modeling with high efficiency This 1s the version 2 0 of CCHE2D mesh generator and it will be improved by adapting new techniques References CCHE Mesh Generator 10 11 12 References Akcelik V Jaramaz B and Ghattas 2001 Nearly Orthogonal Two Dimensional Grid Generation with Aspect Ratio Control J Comput Phys 171 pp 805 821 Ascoli E P Dandy D S and Leal L G 1987 Distortion Function for the strong Constrain Method of Numerically Generatiing Orthogonal Coordinate Grids J Comput Phys v72 513 Duraiswami and Prosperetti A 1992 Orthogonal Mapping in Two Dimensions J Comput Phys v98 254 Eca 1996 20 Orthogonal Grid Generation with Boundary Point Distribution Control J Comput Phys v125 440 Ferziger Jeol and Peric Milovan 1997 Computational Methods for Fluid Dynamics Springer New York Fletcher C A J 1992 Computaional Techniques for Fluid Dynamics Springer Kang LS and Leal L G 1992 Orthogonal Grid Generation in a 2D Domain via the Boundary Integral Technique J Comput Phys v82 269 S rli Karstein 1999 Bounda
37. in later section The Orthogonality Smoothness Adaptivity parameters are required for both Poisson and Variational method and the Iteration parameter 15 required for all the methods except the algebraic method these parameters have default values Note that for the smoothing methods Iteration parameter 15 recommended to be less than 10 to avoid the distortion caused by excessive smoothing especially for complicated cases because Smoothing can be performed repeatedly and the user can improve the mesh gradually 3 Display group This group provides different ways to view mesh In this group there are six commands Bnd Mesh Bed Grided Bed 3D Node and section and three scroll bars for 3D view X Y and zZ Click Bnd the boundary will be displayed Click Mesh the mesh of the selected block will be shown Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 20 e Click Bed once the color shaded bed form will be displayed and the caption of this button will turn into Grided Bed Click this button again the color shaded bed with mesh on will be displayed and the caption of this button will turn into Bed e Click 3D the 3 dimensional geometry of the domain will be shown and three scroll bars will be activated The user can rotate the 3D topography with the
38. me and the 3D topography without mesh will be shown The user can rotate the 3D topography by moving the three scroll bars X Y and Z The user can also increase the scale in Z direction by clicking lt gt button and decrease it by clicking gt button Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 63 a 3D Topography by increasing Z scale b 3D Topography by decreasing Z scale Fig 3 51 3D Topography 3 5 4 View Mesh Nodes Click Node and the mesh nodes colored due to bed elevation will be shown Fig 3 52 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 64 Lr n ar m w i um onm m un tuna M 1 Fig 3 52 Mesh Nodes 3 5 5 View Cross Section The user can view the cross sections through the cross section sub window e Click option and the transverse cross section will be shown while click J option and the longitudinal cross section will be shown The user can move the scroll and change the label of the cross section to be shown Check Multi and up to five cross sections will be shown at the same time Multi No means the number of the sections the user wants to show at the same time Five colors have already been assigned to these five cross sections Of course the user can specify these five cross sections by changing the labels of them e The user can also choose different types of X
39. moothing piar Fig 3 16 Set Skin Click Exit and the user will quit the mesh generator View Menu Click Zoom In and the user can specify one area he wants to see in detail e Click Zoom Out and the user can zoom out the picture e Click Pan and the user can move picture Click Locator and two cross lines will be shown whose intercross point moves with the mouse e Click Restore and the picture will be restored into full screen state Topography Menu This menu consists of two levels The first level is main menu and the components are as follows Click Load Geometry Database a geometry database file will be opened and the survey points colored due to bed elevation will be shown mesh xyz Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 29 Click Load Topographic Image and an image file bmp will be opened Click Coordinates Transformation and a window will pop out which is used to transform the local coordinate of the screen into the real coordinate of the topographic map Coordinates Transformation x Cancel Reference Foint No 1 5 Local Point No 1 wp Fig 3 17 Coordinates Transformation The second level menu is the sub menus of Interpolate Topography 3 2 Click Interpolate Random and bed interpolation based random survey d
40. n to take the advantage of each other The interactive GUI is important to make the combination efficiently In this chapter the mesh generation methodologies are described and the GUI will be introduced in the next chapter Chapter 2 Mesh Generation CCHE Mesh Generator 3 2 1 Algebraic Mesh The algebraic generator adopted here is to create the mesh points in the computational domain by interpolating the nodes according to the nodal distribution along the boundaries of the domain Stretching functions are used to distribute computational nodes along boundaries with several control parameters The distribution for a specific problem should be determined by experienced engineers according to the conditions of flow boundary shape etc Interpolation 15 simply to connect the corresponding nodes along opposite sides with straight lines 2 1 1 Stretching Function The stretching function used in the algebraic method 15 to control the distribution of points on one curved or straight line Equation 2 1 shows the so called one direction stretching function This kind of stretching function can make the distribution of points along on one line with monotonically increasing or decreasing spacing k l S T for k 1 2 1 j 1 S for k Z1 2 1b 1 where S is relative location and k is density parameter When k lt or gt 1 the spacing of points will be decreased unchanged and increased respe
41. nal domain can be generated as a whole or as a collection of several separated sub domains blocks The generation steps illustrated here applies to one sub domain single block if several sub domains multi blocks are involved or to the whole domain if it is not divided Basically four steps are needed to generate an algebraic mesh Step 1 Place the geometry control points along the boundaries Then the domain is divided into several subsections Fig 2 3 In the CCHE mesh generator two kinds of boundaries are identified external boundary and internal boundary According to the Chapter 2 Mesh Generation CCHE Mesh Generator 6 location external boundary consists of four kinds of boundaries namely left boundary right boundary top boundary and bottom boundary Fig 2 4 Control points Fig 2 3 Subsections top boundary Internal boundary right boundary left boundary flow bottom boundary Fig 2 4 Boundaries Step 2 Distribute the mesh control lines along the top and bottom boundaries Fig 2 5 The stretching function is used to distribute the mesh control lines along the me cse mesh control lines boundaries Fig 2 5 Mesh Control Lines Chapter 2 Mesh Generation CCHE Mesh Generator 7 Step 3 Interpolate the interior nodes Fig 2 6 The stretching function is used to distribute the interior nodes in the transverse direction LIT
42. nt 5 Based on the refined database use the inverse distance method to interpolate the bed elevation Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 17 Chapter 3 Interface of CCHE2D Mesh Generator In order to generate computational mesh efficiently with the CCHE2D Mesh generator a Graphic Users Interface GUI is developed This powerful interface is designed to be user friendly interactive and efficient 3 1 Introduction of Interface Fig 3 1 shows the GUI of CCHE2D Mesh Generator It is composed of a big graphic window and operations for mesh generation which are grouped into several categories 0 C Dox nts and Settings yzhang My Documents mesh ms 0607_2002 ms 50060 rator v2 Fie View EIE MEAs QAQA M 7 rr CCHE D Mesh Generator v2 0 Fal 8230 773733 y 25880 825600 Fig 3 1 Interface of CCHE2D Mesh Generator Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 18 3 1 1 Groups of Main Window As Fig 3 1 shows almost all the commands the inputting parameters and the labels are placed group by group on the front face of the main window for easy access These groups of commands and parameters are introduced as follows 1 Block group In this group the user can select the block sub domain and specify mesh size x Jna for this block sub domain After finishing mesh generation max for several blocks sub domains click
43. oint in the bed elevation database closest to this mesh point 15 selected Fig 2 9 Searching Surrounding Points The interpolation is performed to obtain the bed elevation at the mesh point according to g x yee m x y LE 2 19 d where m x y is the bed elevation of the mesh point g x y is the bed elevation of the surrounding points Chapter 2 Mesh Generation CCHE Mesh Generator 16 15 the distance between each surrounding point and the interpolated mesh point n 15 the power Structured Database If the structured survey database is available in order to improve the accuracy of the interpolation a refined database 15 created considering that channel thalweg should be connected Creating such a refined database involves the following steps 1 Refine the data points in the transverse direction along each cross section using linear interpolation and make the number of points on each cross section equal to 2 x Npmax Npmax is the maximum number of points of the cross section in the original database This 1s the first refinement 2 Find the thalweg point of each refined cross section 3 The thalweg point divides each cross section into two parts In each part use the linear interpolation to create Npmax data points This 1s the second refinement 4 According to the latest database linear interpolation 15 used to create data points between two cross sections This 1s the last refineme
44. om Gut 3 han94 1 mesh bnd Pan 4 520 norm 3d mesh bnd M Exit Set Skins Restore Topography Load Topographic Database interpolate Random Hees Iryterpolate Sstricturedj Topographic Coordinates Transtormation Interpolate Topograghy Smooth Fig 3 15 Menus Menu There are files history displayed in the File menu and the user can click them and open them directly Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 27 Click Open Bnd File a boundary file that defines the control points along the domain boundaries will be opened and the domain will be drawn mesh bnd e Click Save as Bnd File a boundary file that defines the control points along domain boundaries will be saved mesh bnd e Click Open Geo File a geo file of an existing mesh will be opened geo Click Open WorkSpace a mesh work space file will be opened mesh wsp Click Save WorkSpace and the current workspace will be saved Click Save as WorkSpace the mesh with all its parameters will be saved as a mesh work space file e Click Save Geo File the current mesh will be saved as a geo file e Click Save as Geo File current mesh will be save as another geo file Click Print and the current picture will be printed out Click Print Preview and a preview window will pop
45. other non uniform mesh is obtained Fig 3 37 Fig3 37 Non uniform Mesh of Block 2 2 Step 3 Generate the mesh for block 1 Set the mesh size 7 18 x 45 and then click Algebraic Fig 3 38 Note that the contraction point set in block 2 are also Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 49 extended to both in block 1 and block 3 The automatic distribution will be used for each subsection in block 1 so make sure to uncheck the Manual Distribution otherwise all other distribution settings in block 2 will be used in this block Fig 3 38 Mesh of Block 1 Step 4 Generate the mesh for block 3 Evaluate mesh size x Jma 33 x 45 and then click Algebraic Fig 3 39 Step 5 Connect the meshes of each block Click Connect and a complete mesh is obtained Fig 3 40 Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 50 Fig 3 39 Mesh of Block 3 Fig 3 40 The Complete Mesh Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 51 Step 6 Interpolate the bed elevation The file with the extension mesh xyz 15 identified as the bathymetry database file which 1s used to interpolate the bed elevation The format of this file is shown in Tab 3 6 Tab 3 6 Format of mesh xyz file No of Total Points Currently two interpolation methods are used in CCHE mesh generator For non structured survey data the inverse distanc
46. r 55 Chapter 3 Inteface of CCHE Mesh Generator fo PSE ORE ee BER RR eee CTT Fig 3 44 rectangular domain in I Direction 10n in 3 3 1 Apply Stretching Funct In I direction in default there 15 only one sub section As shown in Fig 3 44 one can apply the stretching function for all I lines or just one specific I line by choosing option I Line Stretching 3 E Contract No Ph APE lsh zi a for all I lines Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 56 Stretching oJ 1 Contract 18 Ph aee gt b for No 18 I line Fig 3 45 In this example because it s required the contractions at line EF one needs to add contraction point in this direction The contraction points also divide I line into several sub sections where the stretching function is used N C P represents the number of contraction points added in I direction L C P represents the labels of sub sections created by the contraction points R L C P represents the relative location of the contraction points and it is in the range of 0 and 1 that is 0 lt RL C P lt 1 represents the number of I lines in the selected sub section As shown in Fig 3 45 first click option I Line and option Contraction in group of stretching function and then evaluate the parameters in pink color Stretching Stretching
47. r Stokes Equations for mass momentum pollutant and energy conservation Since they are highly non linear the analytical solutions in general cannot be found Numerical solutions can be computed based on discretized equations and the discretization 15 dependent on the mesh which approximates the entire irregular complicated domain Since mesh generation is a time consuming and tedious process which requires handling large amounts of data transformation and solving partial differential equations a mesh generation 15 necessary which can not only make all the involved calculations but also handles the parameters input and the results displayed More importantly mesh generation 15 a process that is problem dependent and needs human intelligence involvement It 1s therefore an interactive process The GUI of the mesh generator provides such a tool for researchers and engineers to generate the mesh efficiently Both the mathematical methods involved and the GUI of NCCHE2D Mesh Generator are introduced Chapter 2 discusses in detail the mathematical methods of mesh generation including the algebraic method the Poisson equation based numerical method the Variational numerical method and the Laplacian smoothing methods etc Chapter 3 introduces the GUI A typical example is given to demonstrate how to generate a mesh step by step This mesh generator has been developed under the supervision of Dr Sam S Y Wang Director of NCCHE and Dr
48. ry Control in Elliptic grid generation Thomas P D and Middlecoff 1980 Direct Control of the Grid Point Distribution in Meshes Generated by Elliptic Systems v18 No 6 pp 652 657 Thompson J F and Johnson 1985 Development of an Adpative Boundary fitted Coordinate Code for Use in Costal and Estuarine Areas Miscellaneous paper HL 85 5 US Army Engineer Waterways Experiment station Vicksburg MS Thompson Warsi Z U A and Mastin C Wayne 1985 Numerical Grid Generation Foundation and Application North Holland New York Thompson J F Soni B K Weatherill and N P Nigel 1998 Handbook of Grid Generation CRC press New York References CCHE Mesh Generator 13 Thompson J F 1996 A Reflection on Grid Generation in the 90s Trends Needs and Influences 5th International Conference on Grid Generation CFS Mississippi State University
49. s mb nisland maximum number of islands mb ncdike maximum number of compound dikes control points of block k mb number of control points of block k mb bnd k 4 boundary type of the four faces of block k amp xcb k n x coordinate of n th control point on the bottom boundary of block k ycb k n y coordinate of n th control point on the bottom boundary of block k xct k n x coordinate of n th control point on the top boundary of block k yct k n y coordinate of n th control point on the top boundary of block k right dikes two lined dike mb nrd k number of right dikes x 2 in block k lid_rd k n relative location of the right dike n in block k Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 71 xdf k n x coordinate of the first control point of the right dike n in block k ydf k n y coordinate of the first control point of the right dike n in block k xdl k n x coordinate of the last control point of the right dike n in block k ydl k n x coordinate of the last control point of the right dike n in block k islands mb nh k number of islands in block k mb_nhc k n number of control points of island n in block k lid nh k n m relative location of m th pair of control points of island n in block k xhb k n m x coordinate of m th control point on bottom boundary of island n in block k yhb k n
50. se scroll bars Click Node the mesh nodes colored according to bed elevation will be displayed e Click a sub window will pop out and the cross sections will be displayed Details will be covered in later section Display Bnd Hesh Bed Fig 3 4 Display Group 4 Tool Bar group This is a collection of tools for editing BTA c 0 4 o A Fig 3 5 Edit Group Each button is represented by a graphical icon and they can be grouped into three functional categories Mesh Information Mesh Editing and Mesh Viewing Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 21 e Mesh Information Probe Data Display Labels of Control Points M T v Evaluate Mesh Edit Properties of Mesh Node Fig 3 6 Tools for Mesh Information The Probe Data button provides nodal information When the mouse moves on the mesh face the user can get the local mesh information simultaneously The local information displayed is 1 J indices G global number of node X Y Z coordinates I D nodal type and n Manning s Roughness n A Tp TUA X AS 7128 DA X 97 JS Xd 499 B920708 oy Fig 3 7 Local information window Click Evaluate Mesh button and the user can get a brief evaluation of the mesh Currently two indicators of mesh quality are identified Smoothness and Orthogonality
51. sh Generator 69 Read 11 mb nrdike mb nisland mb ncdike input data block by block DO 1 1 mb imax DO j 1 mb jmax 1 1 mb_jmax j input control points of the block k Read 11 mb nc k Read 11 mb bnd k 1 mb bnd k 2 mb bnd k 3 mb bnd k 4 DO n 1 mb Read 11 n xcb k n ycb k n xct k n yct k n ENDDO input right dike Read 11 mb nrd k DO n 1 INT mb nrd k 2 Read 11 n n2 xdfl ydfl xdll ydll xdf2 vdf2 xdl2 ydl2 Lid rd k 2 n 1 n2 Lid rd k 2 n n2 1 xdf k 2 n 1 ydf k 2 n 1 ydfl xdl k 2 n 1 ydl k 2 n 1 ydll xdf k 2 n xdf2 ydf k 2 n ydf2 xdl k 2 xdl2 ydl k 2 n ydl2 ENDDO 1nput island Read 11 mb nh k DO n 1 mb nh k Read 11 mb nhc k n DO m 1 mb nhe k n Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 70 11 lid nh k n m xhb k n m yhb k n m Xht k n m yht k n m ENDDO ENDDO input compound dike Read 11 mb_ncd k DO n 1 mb ned k Read 11 id_cd k n id_bnd k n jJ jj 1 4 Read 11 lid_cd k n xed k n jj yed k n Jj jj 1 3 ENDDO ENDDO ENDDO The variables in the above Fortran code are global information mb imax maximum number of blocks in 1 direction mb jmax maximum number of blocks in j direction mb npmax maximum number of control points for all blocks mb nrdike maximum number of right dike
52. sland group In current version the Unstructured Bnd group is disabled Structured Bnd The multi block scheme 15 applied in CCHE2D mesh generator and the Structured Bnd means that the blocks are arranged in a same way as the structured mesh Apart from a global number each block has the I J indices to be uniquely identified The user needs to click Structured Bnd button to activate this group This group provides the operations to create a structured multi block boundary In this group there are six inputting boxes and two options and they are and J are the indices of the current block e Block 15 the global number of the current block e Option Top Boundary means that the operation is worked on the top boundary of the current block Option Bottom Boundary means that the operation is worked on the bottom boundary of the current block Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 31 e records the number of control points of the current block e X 15 the x coordinate of the control point of the current block Y is the y coordinate of the control point of the current block Island In each block the user can add islands into it which is provided by island group The user needs to click Add Island to activate this group and switches from block operation to island operation Note that the island can be added into only the
53. stem of the screen into the real coordinate system of the topographic map Click Topography menu and choose Coordinates Transformation The user can make the transformation as follows 1 click the first reference point on the topographic map and input the real coordinates of this points 2 click the second reference point on the topographic map and input the real coordinates of this points 3 click OK button of the Coordinates Transformation window and the transformation parameter will be shown Local Point MNa 1 1556 929661 2433 559889 Ames AINE X H Ee a H Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 41 Reference Point No 2 2360 0 Local Point No 2 1650 400044 2119 361679 dou ios S E A P E EN AN A E Seta E ead AI age eee ee 7 7 Fig 3 29 Click the Second Reference Point Coordinates Transformation Transformation Parameters Angle 538 Trans 38 821 Scale 7 459 i Trans 000 Fig 3 30 Transformation Parameters Step 4 Click Save and save all the information as a boundary file 3 2 3 Generate Mesh from Boundary File Basically if the boundary file is ready and the default values of the parameters are used it S very easy to generate a mesh What a user ne
54. stretching parameters for each subsection Check Manual Distribution and adjust the parameters section by section Tab 3 4 Tab 3 4 Parameters of each subsections Subl Sub2 Sub3 Sub4 Sub5 I 9 1 3 3 3 8 Chapter 3 Inteface of Mesh Generator CCHE Mesh Generator 47 Stretching Stretching 3 1 Contract 3 1 Contract 1 0 18 o P H 0 015 18 Iv Manually No of J Lines 3 M Manually No of J Lines 37 ara y j auaa Stretching 3 1 Contract sib x Iv Manually No of J Lines Fig 3 34 Parameters of each subsection Now click Algebraic again and a non uniform mesh is obtained Fig 3 35 Fig 3 35 Non uniform mesh of Block 2 1 However the mesh lines are also required to be contracted to the tip in the transverse direction Thus the tip is considered as a contraction point which divides the cross section into two parts In each part the stretching parameters are to be evaluated R L C P is defined as the ratio of the distance from the contraction point to the Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 48 downward boundary to the width of the cross section where the contraction point 15 located Tab 3 5 Parameters of each part Fig 3 36 Parameters of Contraction Click Algebraic again and an
55. th the button Boundary and Move Node become yellow 2 Click the control point you want to move and hold it Move it to the desired place and then release it 3 Repeat step 2 and you can edit more control points 4 Click Save as Bnd File of menu File and all the changes will be saved into a Bnd file 3 4 2 Adjust Mesh Nodes or Lines Location Chapter 3 Inteface of CCHE Mesh Generator CCHE Mesh Generator 59 When the mesh is completed the Edit functions are available for adjusting local nodal distribution Click Move Node and then click the node to be moved Hold the left button of the mouse and move the node to the desired location Note that only the internal nodes can be moved If you want to move the boundary nodes click boundary and then you can move both the internal nodes and the boundary nodes e Click Add I Line or Add J Line and then click the location where one Z line or J line 15 to be added one line or J line will be added into mesh Note make sure the location clicked 15 within the mesh otherwise nothing will happen e Click Delete I Line or Delete J Line and then choose the 7 line or J line 15 to be deleted click 1t and then this line will be excluded Click Undo and the changes of the previous step will be erased Click Save Change all the changes made since the last save change will be saved Note that the ch
56. the weighting function 15 large the mesh size J should be small The weighting function w can be selected which 1s usually evaluated by water depth and bed slope If the numerical solutions such as concentration or velocity gradients are selected the mesh shall be changed dynamically with the numerical solution Uniformity of the mesh 15 measured by the functional I JIVE n Va Q 13 and the orthogonality is defined as I VE Vny Pda 2 14 where the factor J is added to enforce orthogonality with higher weighty value in large cells If the three indices approach their minimum values the mesh would have the highest uniformity orthogonality and adaptivity In general a mesh can be generated by minimizing the sum of the three integrals IT A 1 41 AM 2 15 Chapter 2 Mesh Generation CCHE Mesh Generator 12 Since it 1s impossible to achieve these three objectives at the same time for a particular mesh one needs to select the appropriate combination of the coefficients of 4 4 and Ay According to Brackbill and Saltzman 1982 the 2 D Euler Lagrange equations to solve this variational problem are as follows 4 2 bx I EH C Jew eg TO Vee T Co Ve T Cu Ym w Oy 2 16a 2 16b It is a Poisson equation system and can be solved with any iterative technique For completeness
57. tion of Contraction or repulsion Point N J L means No of J Lines distributed in each contracted or repulsed section Chapter 3 Inteface of Mesh Generator CCHE Mesh Generator 25 3 1 2 Control Panel In current version of CCHE2D Mesh Generator a control panel 15 newly added into the interface which 1s designed to adjust the location of operation controls on the interface Under the low resolution for example 800x600 some controls may not visible and then this control panel can be used to pull out those invisible controls and make them visible Click all the controls move leftward with the same distance e Click all controls move rightward with the same distance e Click 4 all the controls move upward with the same distance e Click _ all the controls move downward left with the same distance Block gt Connect 10 10 T Gener mh Poisson Loploce Lnpacinn V nrintinnal Bed Itpration ithogonality fia Adapiivity 1 0 Mensurad x 5actions Smoothing _1 Contract sis Innunlhy No of gw Black o Bock i Connect Gaenarabe Poisson Laplace _ Lapacian N nrintinnal Bed Orthagonalty fio Smootmness ro Adaptivity 10 Measured X Saections
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