HIVEL 2D v2.0
Contents
1. Appendix B Boundary Conditiions 41 Hivel2D users manual Case 3 Flow regime Subcritical upstream Supercritical downstream Boundary conditions p q specified upstream Case 4 Flow regime Subcritical upstream Subcritical downstream Boundary conditions p q specified upstream h specified downstream Comments This problem may take a long time to reach steady state Case 5 Flow regime Subcritical upstream Subcritical downstream Boundary conditions p q Specified upstream h specified downstream Comments Even though this con tains a steep section in which the flow is Figure B3 Case 3 sketch Figure B4 Case 4 sketch S apy ye 7 Ty O a T A Figure B5 Case 5 sketch supercritical the boundary conditions are the same as for Case 4 The tailwater specified downstream causes the hydraulic jump Appendix B Boundary Conditiions 42 Hivel2D users manual Flow In No Flow Out Case 6 Flow regime Supercritical upstream Wall downstream Boundary conditions p q h upstream Leave out BO lines BI and BO defined in Table 1 Comments Figure B6 Case 6 sketch No steady state keeps filling Note the moving jump that forms Case 7 Flow regime Subcritical upstream Wall downstream Boundary Conditions p q specified upstream Leave out BO lines in geo file Comments There is no steady F state answer just Figure B7 Case 7 sketch keeps filling2. Repeat BEGSCL and BEGVEC sequences for each data set Figure A7 ASCII Vector Data Set File Format DATASET OBJTYPE mesh2d BEGSCL ND 8 NC 8 NAME water surface TS 0 1 00000000e 00 0 00000000e 00 0 00000000e 00 0 00000000e 00 3 24000000e 00 4 39000000e 00 2 96000000e 00 7 48000000e 00 0 00000000e 00 ENDDS Figure A8 Sample ASCII Scalar Data Set DATASET OBJTYPE mesh2d BEGVEC OBJID 27211 ND 8 NC 8 NAME velocity TS 0 1 00000000e 00 5 692781 5 649887 5 726238 5 683091 5 768243 5 724780 5 780255 5 736701 5 769043 5 725574 5 728620 5 685455 5 698828 5 655888 5 682499 5 573179 ENDDS Figure A9 Sample ASCII Vector Data Set Appendix A File Formats 40 Hivel2D users manual Appendix B Boundary Conditions Flow In and Out Case 1 Flow regime Supercritical upstream Supercritical downstream Boundary conditions p q h specified upstream defined in Chapter 2 Comments It can be difficult to get the outflow boundary to Figure B1 Case 1 sketch converge at startup One method is to specify a tailwater such that the flow is barely subcritical then after some time when the resulting jump is nearly gone remove the downstream boundary condition Note F inflow Froude number F outflow Froude number Case 2 Flow regime Supercritical upstream Subcritical downstream Boundary conditions p q h specified upstream h specified downstream Figure B2 Case 2 sketch
3. 2y y 7 Yi XY Yo X3Y1 TRN Va X3Y2 Ys XY ET Yo X27 Ys Xy Appendix E Interpolation Program 56 Hivel2D users manual Interpolation Once the target node has been located and mapped onto old grid element local coordinates x and h the interpolated values of p g and h are found using the following equations h oh E7 p op E8 a 9 4 E9 where n is the number of nodes on the old grid element and f is the appropriate interpolation function Appendix E Interpolation Program 57
4. Chapter 3 Developing an Application 11 Hivel2D users manual Remember the following general rules when generating the grid a HIVEL2D uses linear elements Therefore when generating a HIVEL2D grid use only four node quadrilaterals and three node triangles b Keep the element aspect ratio less than 3 1 the closer to 1 1 the better The aspect ratio is the ratio of the longest element dimension to the shortest i e the length to width ratio c Use gradual transitions in element size Generally an element s area should not be greater than 11 2 times its smallest neighbor d Include at least five or six elements across a channel in the area of interest If for example the channel has an island in the center this resolution is needed on both sides of the island Also increase the resolution around grade breaks and wall transitions Once the grid generation is complete be sure to renumber the grid using SMS renumber options The best numbering scheme will give the smallest bandwidth Normally the nodes need to be numbered progressively across the narrowest dimension of the grid This minimizes the bandwidth which makes HIVEL2D run more efficiently Keep in mind that the model is expecting a relatively narrow computationally dimension across the channel All input is free field The various lines can appear in any order Any prefixes on each line that are not required by HIVEL2D are printed to the screen but are otherwi
5. Superfile S bridge sup Prefix for all files Update Input Filenames Output Filenames Hot start x hot Geometry fx bridge f WS solution pe wsurface dat Flow solution Pe velocity dat Cancel Superfile Figure 3 3 Save Simulation Hot Start The hot start file necessary for the simulation is created using the Build Hot Start dialog fig 3 4 Model Control The hydrodynamic and computation parameter input file contains the hydraulic information about the run the designation of boundary inflow and outflow nodes as well as the computation parameters The dialog Model control fig 3 5 assigns the various hydrodynamic and computation parameter for the model run Chapter 3 Developing an Application 18 Hivel2D users manual Setup HIVEL Hot Start File Figure 3 4 Hot Start Boundary Conditions The inflow Boundary conditions can be assigned using the Assign Boundary Conditions dialog by selecting a specific node for assigning nodal boundary conditions fig 3 6 or by selecting a node string for assigning the node string boundary conditions fig 3 7 The outflow boundary conditions are assigned only using the node string option fig 3 7 A detailed description of the boundary conditions are given in Appendix B Existing nodal or node string boundary conditions can be deleted using the Delete Boundary Conditions dialog Chapter 3 Developing an Application 19 Hivel2D users manual HI VEL
6. Waterways Experiment Station HIVEL 2D v2 0 Users Manual Hivel 2D is a product of the Coastal and Hydraulics Laboratory CHL of Waterways Experiment Station Last Revision March 1 1997 The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products Contents Ve TAO AC CON Soa TaSg4c 1 90342 Ta edegi nsira e eaiail eiaei 1 Background essene i e EE cadet wae eae eee a 1 P rpose and Scopen eaae eE e E a a E 1 2 HIVEL2D OVervViEW an eren E E O te ys EARR 3 Goyer SBGualonsc sees s ese Gwe eee Oe Wee 3 Finite Element Model sees 6 Petrov Galerkin Test Function esse esse eee 7 SHOCK e T 7 Temporal TerVYa NGR i sso hte cE eeen ea iae TS Z eateries tah ae TET af Solution of the Nonlinear Equations sese eee eee eee 8 Model STT 8 3 Developing an Application eeeecesseeceneeeesseeceseeeceneeeesseeeesaees 11 Grid Generauion 22a eee ea stake cea eRe 11 Hydrodynamic npu sss essen 12 STs s ST 13 Ruining the Modelo soree naene o aed e ia Ge eae oes 14 Hiyel Interface enerne ea ace E E cca ON deal 16 Super THT 17 Hot Starten a T a Satacatt
7. No Flow In Flow Out Case 8 Flow regime Wall upstream Supercritical downstream Boundary conditions Leave out BI lines Figure B8 Case 8 sketch Appendix B Boundary Conditiions 43 Hivel2D users manual Comments No steady state goes dry This is probably a very hard problem to run Case 9 Flow regime Wall upstream Subcritical downstream Boundary conditions Leave out BI lines Specify h downstream Comments No steady state goes dry This is also a very hard problem to run Figure B9 Case 9 sketch No Flow In or Out Case 10 Flow regime Wall upstream Wall downstream Boundary conditions Leave out BI and BO lines Figure B10 Case 10 sketch Appendix B Boundary Conditiions 44 Hivel2D users manual Appendix C Troubleshooting Table C1 Problems and Solutions Problem Possible Solutions 1 Model won t converge Try more iterations per time step Reduce time step If lower boundary is migrating away from solution First set a tailwater wait until jump is nearly gone then remove tailwater boundary condition Call for help be prepared to send the geometry hydraulic input output and hot start files 2 Model keeps filling up water Make sure you didn t leave out BO level continuously rises lines in geometry file Use BO and not BO zero Table 1 3 Converges to a bizarre Make sure resolution is adequate solution 4 Problems reading hot start Verify that the t
8. Model Control Ed Job Titles Title 1 IEE Title 2 Solver using SMS 5 0 Title 3 JLet s see how thsi works Turbulence Coefficients Units Iterations 0 1000 Normal smooth English units Max of iter timestep 0 2000 Near jump rough Metric units 0 0050 Froude convergence tol Computation Time 1 0000 Time step a tine Save output every nd timestep Temporal Derivative First order backward Second order backward _ Specify Petrov Galerkin coeffs Upstream weighting of the test function in j0 2500 Smooth regions 0 5000 Rough regions 32 1890 Gravitational acceleration ig 2 2080 Conversion coeff for Manning s n Co 2 Reset Defaults Cancel Figure 3 5 Model control HIYEL Nodal Boundary Condition Ed Flow Type Subcritical Supercritical Inflow Parameters Velocity components Unit discharge components Cancel Figure 3 6 Nodal Boundary Conditions Chapter 3 Developing an Application 20 Hivel2D users manual HI VEL Nodestring Boundary Condition x Flow Type Subctitical Supercritical Boundary Type Inflow string Outflow string Inflow Parameters ve ocity components jo c000 T Unit discharge components jooo y obeh To Elevation Outflow Parameters 30 0000 Tailwater elevation Figure 3 7 Node String Boundary Conditions Model Checke
9. are as follows a Combinations of linear based triangular and rectilinear shape functions are used to represent p q and h Chapter 2 HIVEL 2D overview 8 Hivel2D users manual b The model is compiled to solve problems having meshes as large as 2000 nodes and 2000 elements and will run on a IBM compatible personal computer having at least 8 MB of RAM c A Newton Raphson iteration is used within each time step d The mild slope assumption is invoked This means the slope should be less than about 0 05 This assumes that the slope is geometrically mild not hydraulically mild e Boundary conditions are specified for any combination of supercritical and subcritical inflow and outflow L Boundary conditions are constant over the simulation period g Boundary roughness Manning s n is specified on an element type basis h A user specified parameter produces either first order or second order backward temporal differences i A Petrov Galerkin approach in which the test function is weighted upwind along characteristics is employed The degree of upwinding and thus stability is determined by the parameters B and By Defaults are B 0 25 and B 0 5 j A shock detection mechanism based upon the energy variation per element is used to invoke By k Turbulent eddy viscosity is calculated based upon simple user specified parameters Ceu and Cs using velocity depth and roughness Chapter 2 HIVEL 2D overview 9 Hivel2D
10. files are stored in a 2D GEO file The file format is shown in Figure A5 A sample geometry file is shown in figure D3 Appendix D Gravitational Acceleration Conversion coefficient for manning s n Turbulence coefficients for smooth and rough region Time step and temporal derivative order Number of time steps and interval Number of iterations and convergence criteria Petrov Galerkin coefficients for model stability Inflow locations by nodes Inflow locations by string Outflow locations by string Material type and manning s n for each Figure A5 2D Geometry File Format Appendix A File Formats 31 Hivel2D users manual The card type used in the hydrodynamic flow file are as follows Description Gravitational acceleration Required Yes Format GRAV g Sample GRAV 32 2 1 Gravitational acceleration in the units of your choice Description Conversion coefficient for Manning s n formulation 2 208 for English units and 1 0 for Metric units Required Yes Format MCON c2 1 1 486 for English 1 000 for Metric Appendix A File Formats 32 Hivel2D users manual Sample TURB 0 10 0 50 1 csb 0 1 1 0 coef for smooth regions 0 1 1 0 coef for rough regions Sample Time 1 25 2 00 2 1 00 2 00 1 0 first order backward 2 0 second order Appendix A File Formats 33 Hivel2D users manual HHL H Number of time steps and i
11. interface to HIVEL2D fig 3 1 Several steps are involved in performing a HIVEL simulation within SMS These steps are listed here to provide a summary of the overall process Some of the steps are described in more detail in the following sections The steps are as follows File Edit Display Data Nodes Elements RMA2 SED2D RMAIO FESWMS Window Help New Simulation Open Simulation Save Simulation Build Hot Start Assign BC Delete BC Model Control Material Properties Display Options Model Check Run HIVEL EEZ Bpel DELIS lela LE e lela DE X coordinate Y coordinate Z coordinate No Scalar No Vector No Vector Other Ee 000000 000000 500000 H 7 7 7 Nothing dl Cursor 4111 11 275 45 7 7 7 7 Save the existing HIVEL simulation flo amp geo Figure 3 1 The SMS interface 1 Create a 2D finite element grid to be modeled The tools provided in SMS for constructing a 2D finite element grid are described in SMS users manual This Chapter 3 Developing an Application 16 Hivel2D users manual chapter should be read entirely before generating a 2D grid for use with HIVEL2D 2 Use the commands in the HIVEL menu to define the material properties assign the boundary conditions and to enter the other model parameters 3 Run the HIVEL Model Checker by selecting the Model Check command Fix any errors that are found in your model 4 Select the Save Simulati
12. nodes BIN For the BIS specification the flow vector is defined as a perpendicular to the BIS line say it has to be straight and into the model Format BIS ibist nbi iuorp vxi vyi ihe hi nl n2 Sample BIS 2 4 2 21 23 1 67 1 27 32 111 112 113 n Number of nodes that make up this inflow string 2 Supercritical boundary specify u v h 2 Supercritical boundary specify p q h 1 Subcritical boundary specify u v 1 Subcritical boundary specify p q Either the depth or water surface elevation of this string If this is a subcritical boundary 4 5 vxi vyi x and y components of either velocity or unit discharge depending on iuorp U Depth specified 1 Elevation specified If this is a subcritical boundary this variable is not used a Appendix A File Formats 37 Hivel2D users manual pf this variable is not used Node ids that makeup this ne inflow node string Card Type n Description Inflow location and amount by node Required BIN nd iuorp vxni vyni ihe hni y Sample BIS 363 2 21 23 1 67 27 32 o L a 0 iuorp 2 Supercritical boundary specify u v h 2 Supercritical boundary specify p q h 1 Subcritical boundary specify u v 1 Subcritical boundary specify p q A vxni vyni x and y components of either velocity or unit discharge depending on iuorp 7 hni Depth at the node is specified at supercritical inflows and at subcritical inflows no specification is needed or used O
13. products for all sides are greater than zero then the node lies within that element Interpolation Scheme for Quadrilateral Elements For convenience in interpolating a local coordinate system x h is used where 1 gt L lt l and 1 lt 1 lt 1 Figure El to derive the bilinear interpolation functions First the target point Xp yp is written in x h coordinates Figure E1 Local coordinates for quadrilateral and triangular elements This is done using Newton Raphson iteration to solve the following equations 4 x y xi El i l and y Qy E2 for the local coordinates x and h where the bilinear shape functions for a quadrilateral element are 1 70 d m 0 RT n Appendix E Interpolation Program 54 Hivel2D users manual 1 71 n 1 57 LAAT Interpolation Scheme for Triangular Elements Again the local coordinate system x h where 1 lt amp lt 1 and 1 lt n lt 1 Figure El is used to derive the interpolation functions Solving x 0x E3 and y oy E4 i 1 simultaneously for x and h where 1 SSR 1 50 6 1 30 are the bilinear shape functions for a triangular element results in the following equations for x and h Appendix E Interpolation Program 55 Hivel2D users manual E B o a a pat Q uC Y Y T lt Y Y Yo and S a L E6 CR a a eee Te where O X X Q x hy WNL N B 2x X B
14. users manual Chapter 2 HIVEL 2D overview 10 Hivel2D users manual 3 Developing an Application The basic steps to developing an application of HIVEL2D are as follows a Generate the grid 1 Number the grid intelligently 2 Identify inflows and outflows b Develop a hydrodynamic input file c Develop a reasonable hot start file d Run the model probably several times If necessary refine the grid and interpolate a new hot start file using INTRPL8 EXE Appendix D e View the output files in Surface Water Modeling System SMS or in any other graphical program L Examine the solution for reasonableness Hivel 2D version 2 0 uses SMS Brigham Young University 1997 as the pre and postprocessor for programs involving two dimensional finite element meshes It was developed by the Engineering Computer Graphics Laboratory at Brigham Young University for the U S Army Engineer Waterways Experiment Station Grid Generation To a large degree the quality of the grid determines the accuracy and stability of the model The first step in grid generation is getting the necessary geometry information into the grid generator Critical elements such as points on transitions bridge piers and curves should be put into the grid generator One method involves drawing the structure to be modeled in three dimensions in a CAD program and then extracting the critical points These critical points are then put into a grid generator
15. which is often the case for new cards old files are still compatible If an old card type is no longer used the card can simply be ignored without causing input errors HIVEL2D Super File A HIVEI2D super file is a file which contains a list of other files Each of the files in the list must be one of the basic HIVEL2D file types geometry hydrodynamic flow If a super file is selected using the Read command in the File menu each of the files listed in the super file are opened and read This makes it possible to quickly read in several files at once without having to identify each file individually in the file browser The file format for a super file is shown in Figure A1 The first line in the file is a SUPER card which identifies the file as a super file Each of the other cards shown are optional Each of the cards has a card identifier representing the type of file The Appendix A File Formats 27 Hivel2D users manual identifier is followed by a file name The file name should be a complete path if the file is not in the same directory as the super file Any suffix may be used with the file name A sample super file is shown in Figure A2 filename filename filename filename filename Geometry file Hydrodynamic flow file name Hot Start file First solution file Second solution file Figure Al Super File Format bridge geo bridge flo bridge hot wsol dat vsol dat Figure A2 Sam
16. However if the walls or other structures make a significant contribution to the overall turbulence this equation will underpredict the magnitude of the eddy viscosity or turbulence Even under typical channel configurations there is fairly large uncertainty in the parameter C This is apparent since it has been found to range from 0 1 to 1 0 Therefore the user should consider making a sensitivity check on the calculated water surface for a range of values of C and any other parameters having values that are largely uncertain Chapter 2 HIVEL 2D overview 5 Hivel2D users manual Finite Element Model This system of partial differential equations is solved using the finite element method The finite element approach taken is a Petrov Galerkin formulation that incorporates a combination of the Galerkin test function and a non Galerkin component to control oscillations due to convection An integration by parts procedure is used to develop the weak form of the equations The weak form which facilitates the specification of boundary conditions is LF y 0 479 dy 8 z e dQ 09 99 fly T Qe B32 v Ho Jo Fan P n a 0 where the variables are understood to be discrete values and e subscript indicating a particular element Q domain y 0 1 test function p Galerkin part of the test function I identity matrix 0 non Galerkin part of the test function ny Ny H unit vector outward normal to the
17. MANNING CONVERSION turb 0 1000 0 2000 CB FOR VISCOSITY SMOOTH AND JUMP time 1 0000 1 0000 TIME STEP TEMPORAL DIFF step 20 20 TIME STEPS OUTPUT INTERVAL iter 4 0 00500 INUMB OF ITER CONV CRITERIA bin 12 60 000 0 000 1 3 000 bin 2 2 60 000 0 000 1 3 000 bin 3 2 60 000 0 000 1 3 000 bos 2 0 14 8 6 333 334 335 336 337 338 mtyp 2 NUMBER OF ELEMENT TYPES FOR ROUGHNESS 1 0 0150 2 0 0250 Figure DS Initial hydrodynamic input file example 1 flo was chosen to be first order since the interest is in steady state results only Even though the downstream boundary is intended to be supercritical and no boundary condition is needed experience has shown that the model sometimes will converge to a different solution or be unstable unless a very good starting guess at the solution was made Therefore until the model settles down a tailwater elevation is specified corresponding to flow that is slightly subcritical Two different element types and Manning s roughness coefficients have been designated The convergent section is steeper and rougher in this example The model will run 20 time steps resulting in a simulation time of 20 sec The time step size is then increased Later the downstream tailwater condition is effectively removed by specifying an elevation that is below the bed elevation The nodes 1 2 and 3 are the upstream boundary nodes designated by BIN in the hydrodynamic flow file and nodes 333 338 are
18. bin 2 2 60 000 bin 3 2 60 000 bos 2 0 30 6 333 334 335 336 337 338 mtyp 2 1 0 0150 2 0 0250 GRAVITY FT SEC SEC MANNING CONVERSION CB FOR VISCOSITY SMOOTH AND JUMP TIME STEP TEMPORAL DIFF TIME STEPS OUTPUT INTERVAL INUMB OF ITER CONV CRITERIA 0 000 1 3 000 0 000 1 3 000 0 000 1 3 000 NUMBER OF ELEMENT TYPES FOR ROUGHNESS Figure D7 Final hydrodynamic input file example3 flo Appendix D Example problem 50 Hivel2D users manual perpendicular to the flow instead of being swept back Note also that the flow returns to supercritical flow along the pier sides and a depression wave has the sweptback wake Figure D8 Final water surface contours ft Figure D9 Final velocity contours fps Appendix D Example problem 51 Hivel2D users manual Appendix D Example problem 52 Hivel2D users manual Appendix E Interpolation Program The interpolation program INTRPL8 EXE allows the user to refine a grid for which answers p q and h defined in Chapter 2 have already been found Using the old hot start information the old geometry and the new geometry the user can generate a new hot start file for the new geometry This new hot start file is then the starting point for a new run of HIVEL2D The program also outputs an interpolated plot output file that can be converted to binary and viewed in SMS This is used to verify the inter polated values This feature can als
19. boundary I and re OF Ta oF 9 30 Chapter 2 HIVEL 2D overview 6 Hivel2D users manual Natural boundary conditions are applied to the sidewall boundaries through the weak form The side wall boundaries are no flux boundaries that is there is no net flux of mass or momentum through these boundaries These boundary conditions are enforced through the line integral in the weak form Petrov Galerkin Test Function The Petrov Galerkin test function y is defined Berger 1993 as 9 O1 9 10 og dP 0 ofa a Ay id J 11 ox oy where B is a dissipation coefficient varying in value from 0 to 0 5 the A terms are the linear basis functions and A x and A y are the grid intervals A detailed explanation of this test function in particular A and B is given in Berger 1993 Shock Capturing The coefficient B scales the dissipation needed for numerical stability More dissipation is needed in the vicinity of shocks such as hydraulic jumps than in smooth regions of the flow field Because a lower value of B B f is more precise a large value of P B f 0 5 where B uand B are the Petrov Galerkin parameters for smooth flow and for shocks respectively is applied only in regions in which it is needed HIVEL2D employs a mechanism that detects shocks and increases B automatically Therefore B is implemented only when needed as determined by evaluation of the element energy deviation In a simila
20. e is shown in Figure D3 T1 example geometry file contains 338 nodes representing a bridge pier T2 anda contraction the contraction is steeper and rougher than T3 the rest of the model LeS 2 I 2 4 5 T 8 335 329 328 334 337 331 330 336 338 332 331 337 0 0000 0 0000 0 0000 50 0000 0 0000 100 0000 100 0000 0 0000 100 0000 50 0000 100 0000 100 0000 2000 0000 23 0000 20 0000 2000 0000 41 0000 20 0000 2000 0000 59 0000 20 0000 2000 0000 77 0000 20 0000 2000 0000 95 0000 20 0000 Figure D3 Example geometry file example geo The initial hot start file can be tricky This case involves a straight reach so it is fairly easy to set up a file with p q h of 60 0 3 as a constant throughout the domain If the domain is curved one might have to start with pooled flow at a single depth The beginning of the initial hot start file is shown in Figure D4 The initial input file is shown in Figure D5 The text in the hydrodynamic input file that describes each numerical input is not actually read by the program so it can be left out or changed The initial time step was chosen to produce a CFL number Equation 15 of roughly 1 so this time step is chosen as 1 0 sec The temporal derivative This line is repeated at least 338 times one line for each node Figure D4 Example hot start file example hot Appendix D Example problem 48 Hivel2D users manual grav 32 18900 GRAVITY FT SEC SEC mcon 2 20800
21. e two space directions and time The shallow water equations in conservative form are given as Abbott 1979 a ar ar ee on ae H 0 1 where h Q D 2 Chapter 2 HIVEL 2D overview 3 Hivel2D users manual F gh 3 4 SIR TS 7 5 where p uh u being the depth averaged x direction component of velocity q vh v being the depth averaged y direction component of velocity g acceleration due to gravity Chapter 2 HIVEL 2D overview Hivel2D users manual C XxX 0 50 xy yx Oy Reynolds stresses where the first subscript indicates the direction and the second indicates the axis direction normal to the face on which the stress acts p fluid density Zu channel invert elevation n Manning s roughness coefficient Co dimensional constant Co 1 for SI units and Cg 1 486 for English units The Reynolds stresses are determined using the Boussinesq approach relating stress to the gradient in the mean currents du Ox ADNE ST du du Oy Oy pv 3 T S 6 Oy re yy dy where n is the eddy viscosity which varies spatially and is solved empirically as a function of local flow variables Rodi 1980 CnJ 8gV HD7 q C hi 7 where C is a coefficient that varies between 0 1 and 1 0 The typical high velocity channel is rather wide and shallow so that the bulk of the turbulence is bed generated and therefore Equation 7 is reasonable
22. es Appendix A for file formats are generated as the model output The Data Browser command from the Data menu can be used to Import the solution files for viewing The output file contains the following a The number of time steps saved number of elements and number of nodes b The time c Velocity components of u and v and water surface elevation for each node Note these are repeated for each time step that was output The number of time steps saved is determined by the request in the hydrodynamic input file for calculated time steps and NRVL the interval to save time steps to this file This file can get quite large so assign NRVL with discretion Chapter 3 Developing an Application 23 Hivel2D users manual Chapter 3 Developing an Application 24 Hivel2D users manual References Abbott M B 1979 Computational hydraulics elements of the theory of free surface flows Pitman Advanced Publishing Limited London Berger R C 1993 A finite element scheme for shock capturing Technical Report HL 93 12 U S Army Engineer Waterways Experiment Station Vicksburg MS Brigham Young University 1997 SMS 5 0 MS Windows Version Engineering Computer Graphics Laboratory Brigham Young University Provo UT Rodi W 1980 Turbulence models and their application in hydraulics A state of the art review State of the Art Paper International Association for Hydraulic Research Delft The Nethe
23. ience One method is to start the model with zero velocity and a constant depth The data are read as free field This file will be overwritten by the model run so if there is a chance that this information will be needed later save a copy If the model run finishes but the data are bad for some reason the hot start will be bad as well Again this is a good reason to save a copy The information in the hotstart file is Line 1 TIME Line 2 p q h a T M for each node in order where TIME the time associated with values at time step m m the last time step m l the next to the last time step Remember that this file is free format The initial hot start file can also cause starting a run to be tricky If the interest is in steady state conditions the accuracy of the initial guess will determine how long it will take to reach steady state If the geometry is simple then there is no trouble in guessing the discharge components However if it is complicated it may be necessary to resort to zero discharge and a specified depth which is a typical method If the walls are sloping there may be some difficulty in specifying the depth as well It is fairly simple to write a program to subtract the bed elevation from some set of water surface elevations Typically the user should set the old and the even older time step information in this file as identical Running the Model In this section a general overview for runni
24. ime is included as file the first line of the file Verify the number of lines May have to put a carriage return at the end of the last line of the hot start file Appendix C Troubleshooting 45 Hivel2D users manual Appendix C Troubleshooting 46 Hivel2D users manual Appendix D Example Problem The example grid is shown in Figure D1 The flow enters on the left and exits to the right The 2 000 ft 610 m long model is supercritical at both boundaries so all infor mation is specified at the upstream end The example contains a transition from a 100 ft 30 5 m width to a 90 ft 27 4 m width The slope is 0 01 except in the 100 ft 30 5 m length of transition where it is 0 02 The transition is to have a bed roughness higher than the rest of the model The model includes a 50 ft 15 2 m long by 18 ft 5 5 m wide bridge pier Note that the resolution is concentrated around and downstream of any abrupt changes Figure D2 Since this flow is supercritical all information including shocks and rough conditions is swept downstream Therefore this is where the resolution is needed Figure D1 Complete example grid and geometry Figure D2 Detail of example grid showing transition and bridge pier Appendix D Example problem 47 Hivel2D users manual The complete geometry file includes 338 nodes and 302 elements An abbreviated version of the geometry fil
25. k to select all objects with same warning or error Mesh has not been renumbered since it was read in Possible errors in the HIVEL data none Correct warning or error by performing the following steps Figure 3 8 Model Check Run HIVEL Once a simulation has been created checked and saved the HIVEL2D executable program can be run HIVEL2D can be executed one of two ways from the HIVEL menu in SMS or from the DOS or UNIX command line Launching HIVEL2D from the Menu HIVEL2D can be run from the Hivel menu in SMS using the following procedure 1 Make sure you have saved the simulation using the Save Simulation command 2 Select the Run Hivel command from the Hivel menu Chapter 3 Developing an Application 22 Hivel2D users manual 3 At this point HIVEL2D is launched in a new window prompting the user to type the name of the super file Once the super file name is typed HIVEL2D opens the file and begins the simulation Launching HIVEL2D from the Command Prompt HIVEL2D can be run from DOS UNIX command prompt using the following procedure 1 Make sure you have saved the simulation using the Save Simulation command 2 Open a DOS UNIX shell and the appropriate directory and type the HIVEL2D executable 3 HIVEI2D is launched prompting the user to type the name of the super file Once the super file name is typed HIVEL2D opens the file and begins the simulation Output Files Two ASCII solution fil
26. l is sometimes difficult when the flow is supposed to be supercritical at the outflow boundary The model attempts to converge to a solution but it may not be the desired solution One way to avoid this is to start the model with a tailwater that is slightly subcritical if the starting conditions are not known Then after the model settles down the boundary condition can be changed to supercritical This takes a little experience Users should note that the Manning s n applies to each element type as well as the adjoining sidewalls It is also used in conjunction with velocity depth and C to determine a turbulent eddy viscosity estimate The input to the hydrodynamics file is made through the list in Figure A5 Appendix A All variables are real except those beginning with J J K L M or N which are integer variables All input is free field Each variable is described in Table 2 in the order in which it appears in the hydrodynamic input file Units are designated by L and T for length and time respectively If no units are specified the variable is dimensionless Hot Start File This file is the last two time steps of information from the previous model run Since the temporal derivative can be a second order backward difference two time steps of old information are needed If this is the initial run then this information will have to be Chapter 3 Developing an Application 13 Hivel2D users manual generated based upon exper
27. metry numerical model computational mesh file the hydrodynamic parameters boundary conditions file and the initial conditions file Finally the numerical model output file is explained Appendix A describes the file formats Appendix B describes the boundary conditions Appendix C describes problems with the model and solutions Appendix D gives an example problem Appendix E discusses the interpolation program Chapter 1 Introduction Hivel2D users manual Chapter 1 Introduction Hivel2D users manual 2HIVEL2D Overview HIVEL2D Stockstill and Berger 1994 is designed to simulate flow typical in high velocity channels The model is a finite element description of the two dimensional shallow water equations in conservative form The model does not include Coriolis or wind effects as these are typically not important in high velocity channels Governing Equations Vertical integration of the equations of mass and momentum conservation for incompressible flow with the assumption that vertical accelerations are negligible compared to the acceleration of gravity results in the governing equations commonly referred to as the shallow water equations The dependent variables of the two dimensional fluid motion are defined by the flow depth h the volumetric discharge per unit width in the x direction p and the volumetric discharge per unit width in the y direction q These variables are functions of the independent variables x and y th
28. ndorsement or approval of the use of such commercial products The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products Hivel2D users manual 1 Introduction Background HIVEL2D is a free surface depth averaged two dimensional model designed specifically for flow fields that contain supercritical and subcritical regimes as well as the transitions between the regimes The model provides numerically stable solutions of advection dominated flow fields containing shocks such as oblique standing waves and hydraulic jumps HIVEL2D has been verified by comparing computed model results with laboratory data The findings of these tests are presented in Stockstill and Berger 1994 Purpose and Scope This report serves as a user s manual for HIVEL2D Version 2 0 This user friendly version of the program has been incorporated into SMS Brigham Young University 1997 First a brief description of the model equations are presented Next step by step instructions are given to guide the user in creating the required input files These input files include the geo
29. ng HIVEL2D is described The HIVEL interface in SMS is described in the following section To run the model the user must supply a super file which includes five file names three input and two output The file prefixes follow the name of the super file HIVEL2D is developed and run within SMS a The executable of the model is called HIVEL2D and a copy of it should be in the users working directory b The model application and files are developed launched and viewed within SMS Chapter 3 Developing an Application 14 Hivel2D users manual c Each file name can be up to 15 characters for UNIX and IBM compatibles e g EXAMPLE1 SUP d The file extensions of SUP GEO FLO HOT and DAT are ones that are typically used to designate files but these suffixes are arbitrary e The geometry file contains the node locations and the element connection table L The hydrodynamic and computation parameter input file contains the hydraulic information about the run the designation of boundary inflow and outflow nodes as well as the computation parameters Examples of computation parameters are the specific boundary values of depth and flow rates roughness time step size number of iterations etc g The output files contains the water surface elevation and velocity fields for all nodes at each time location designated in the hydrodynamic input file This information can then be converted to a form that can be viewed in SMS h The hot star
30. nterval for storing output Required Yes STEP nsteps an 4 STEP 50 5 ried 2 nrvl Interval for saving output ie 5 means save time step 5 10 15 CardType ITER __ _ Description Number of iterations per time step and convergence of hee od ie et Format ITER itmax tol mer 5 00005 itmax Maximum number of iterations allowed per time step tol If maximum relative change in nodal Froude number is less than Appendix A File Formats 34 Hivel2D users manual tolerance the code will advance to the next time step 1 sm 0 00 0 50 upstream weighting of the test function in smooth regions areas like shocks Card Type MTYP Number of material types and manning s n for each Format 3 Number of material types 1 continued Material number 2 continued Manning s n for the Appendix A File Formats 35 Hivel2D users manual material Card Type Outflow location list of nodes No if you intend no outflow Format BOS ibost iscsc tail nbo nl n2 BO 2 0 1204 4 470 369 242 0 subcritical outflow read specified tailwater elevation tailwater elevation to be applied along this string of nodes number of nodes that make up this outflow string string of node ids that continuation makeup this outflow Appendix A File Formats Hivel2D users manual The inflow nodes can be specified by either a line of nodes BIS or by individual
31. o be used to interpolate from a fine grid to a coarse grid to better view vectors on a very fine grid for example Users should note that the program cannot interpolate answers for any nodes that lie outside the old geometry s boundary For instance refining a mesh around a curve will cause the nodes along the curve s outer radius to lie outside the old coarse mesh s boundary The program will report the nodes that lie outside the domain Program Description After input of the necessary data the first routine the program performs is that of comparing the old grid with the new grid Old node numbers are typically going to be different than new ones For this reason the old answers at each node are first mapped onto the corresponding nodes on the new grid by comparing the coordinates of the nodes Next comes the task of looking at each node seeing if it is a new node and if itis a new node finding out in which old element it is located There are two possible locations for a new or target node in a quadrilateral element or in a triangular element A node on an element side is interpolated in the element in which it is first found Deciding in which element a target node is located is done by a cross product scheme in which the cross product is taken between a vector lying on the side of an element and Appendix E Interpolation Program 53 Hivel2D users manual a vector from a corner node on that side to the target point If the cross
32. on command to save the model to disk 5 Select the Run HIVEL command to run the simulation 6 Select the Data Browser command from the Data menu and use the Import button to read in the solution files generated by HIVEL 7 Use the SMS post processing tools such as contours and velocity vectors to view the solution Super File A HIVEL2D super file is a special type of file that organizes the set of files used in a simulation The names of all of the input and output files associated with a simulation are saved in the super file When HIVEL2D is executed it prompts the user for the name of the super file Open Look in 4 Sms File name bridge Files of type Default Files sup lt Cancel T Open as read only Help Figure 3 2 Open Simulation Chapter 3 Developing an Application 17 Hivel2D users manual The super file provides HIVEL2D with all of the file names involved in the simulation and no more prompts are necessary Likewise an entire simulation can be imported to SMS at once by opening the super file using the open simulation dialog fig 3 2 The super file name and full path are specified by selecting the Super File button at the top of the Save Simulation dialog which brings up the File Browser The name and location path of the super file are specified The super file and all of the other HIVEL2D input files are stored in the selected directory fig 3 3 HI EL Data Files Ed
33. ple Super File Figure A3 Numbering sequence for quadrilateral and triangular elements Appendix A File Formats 28 Hivel2D users manual 2D Geometry File Two dimensional finite element geometry files are stored in a 2D GEO file The types of elements supported in HIVEL2D and the numbering sequence for the elements are shown in Figure A3 The file format is shown in Figure A4 A sample geometry file is shown in figure D3 Appendix D Tl Title Lines T2 Title Lines T3 Title Lines E3 id n1 n2 n3 mat 3 node triangle EF4idnin2n3n4mat 4 node quad ND idx yz Nodal coordinates Figure A4 2D Geometry File Format The card type used in the 2D geometry file are as follows Sample T1 Sample Problem T2 Charlie Berger T3 3 1 97 aooo o ode ee Appendix A File Formats 29 Hivel2D users manual Description Defines a three node linear triangle element Required No Format E3 id nl n2 n3 mat Sample E3 283 13 32 27 3 2 4 nl n3 The nodal indices of the element ordered counterclockwise 5 mat The material id of the element Description Defines a four node Bi linear quadrilateral i mae 1 E4 id nl n2 n3 n4 mat E4 283 13 32 27 30 3 nl n4 The nodal indices of the element ordered counterclockwise Appendix A File Formats 30 Hivel2D users manual element Sample ND 84 120 4 380 3 5632 0 Hydrodynamic Flow File Two dimensional finite element geometry
34. r Once a grid is generated and all of the analysis options and boundary conditions have been specified the next step is to save the simulation to disk and Run HIVEL However before saving the simulation and running HIVEL the model should be checked with the Model Checker Because of the significant amount of data required for a HIVEL2D simulation it is often easy to neglect important data or to define inconsistent or incompatible options and parameters Such errors will either cause HIVEL2D to crash or to generate an erroneous solution The purpose of the Model Checker is to analyze the input data currently defined for the model simulation and report any obvious errors or potential problems Running the Model Checker successfully does not guarantee that a solution will be correct It simply serves as an initial check on the input data and can save a considerable amount of time that would otherwise be lost tracking down input errors To check the current HIVEL2D data select the Model Check command from the HIVEL menu The Model Check dialog shown in Figure 3 8 will appear To run the Model Checker select the button labeled Run Check at the bottom of the dialog This generates a list of possible errors and warning messages in the top scrolling window Chapter 3 Developing an Application 21 Hivel2D users manual HI VEL Model Checker P Checker Options Save Messages Click to select object and display suggested solution Shift clic
35. r manner the eddy viscosity coef ficient C varies from Ceu to Csy the effect being that eddy viscosity is increased only in areas of greatest element energy deviation Temporal Derivatives A finite difference expression is used for the temporal derivatives The general expression for the temporal derivative of a variable Q is Chapter 2 HIVEL 2D overview 7 Hivel2D users manual 1 nL m m 1 d0 Y l coe OF 0 0 4 12 1 0 j 2 2 rt g t f where j is the nodal location and m is the time step An equal to 1 results in a first order backward difference approximation and an a equal to 2 results in a second order backward difference approximation of the temporal derivative Solution of the Nonlinear Equations The system of nonlinear equations is solved using the Newton Raphson iterative method Let R be a vector of the nonlinear equations computed using a particular test function y and using an assumed value of Qj R is the residual error for a particular test function i Subsequently R is forced toward zero as ORI dQ AQ Rf 13 where the derivatives composing the Jacobian are determined analytically and k is the iteration number This system of equations is solved for A Q and then an improved estimate for Qo is obtained from dY 0 AQ 14 This procedure is continued until convergence to an acceptable residual error is obtained Model Features Particular features of HIVEL2D Version 2 0
36. rlands Stockstill R L and Berger R C 1994 HIVEL2D A two dimensional flow model for high velocity channels Technical Report REMR HY 12 U S Army Engineer Waterways Experiment Station Vicksburg MS References 25 Hivel2D users manual References 26 Hivel2D users manual Appendix A File Formats This section contains the file formats for files used by HIVEL2D The files used by HIVEL2D use a card type format With this format the components of the file are grouped into logical groups called cards The first component of each card is a short name which serves as the card identifier The remaining fields on the line contain the information associated with the card In some cases such as lists a card can use multiple lines There are many advantages associated with the card type approach to formatting files Some of the advantages are 1 Card identifiers make the file easier to read Each input line has a label which helps to identify the data on the line 2 The card names are useful as text strings for searching in a large file All input lines of a particular type can be located quickly using a find command in a text editor 3 Cards allow the data to be input in any order in many cases i e the order that the cards appear in the file is usually not important 4 Cards make it easy to modify a file format New data can be included simply by defining a new card type If the new card is optional
37. se ignored by the program Table 1 shows the geometry file format If the geometry was generated using SMS then the E3 E4 and ND lines are transparent to the user To generate a grid from scratch be sure to follow the correct format shown in Figure A4 Appendix A Hydrodynamic Input Starting the model is usually the most difficult task The model should be started with small time steps i e a CFL number less than 1 where lUl gh Oe MOM 15 where IUI vw Vv Chapter 3 Developing an Application 12 Hivel2D users manual and A l the element length A t the time step size The time step can then be gradually increased If the steady state solution is desired then a fairly large time step can be used If the interest is in unsteady results then for accuracy the CFL number should be held to a maximum of 2 Appropriate boundary conditions must be supplied For an inflow boundary condition when the flow is supercritical the user must specify both x and y components of flow along with the depth If the flow is subcritical here then only the x and y components of flow are read If the flow is subcritical at the outflow boundary then the tailwater elevation must be specified If the flow is supercritical at the outflow then no boundary conditions need to be given This is done in the input file by specifying a tailwater elevation that is lower than the bed elevation at the outflow boundary Starting the mode
38. t file contains the time p g and depth for the last two time steps This is used to start the calculation This file is overwritten by each successful run so if it might be needed later make a copy of it under another name before running the program After the file names are input the program will begin running and several banners will appear on the screen a First the program informs the user of any unused lines in the geometry file and prints the contents of the unused lines b Next the contents of the hydrodynamic input file are displayed on the screen to allow the user to check the values that were read c If the coefficients Csm Csp or are out of range the program will report the error and halt d Then as the program runs the results for each time step are displayed These results include the number of iterations required the maximum residual error and the node with which it is associated the average energy the minimum vorticity and the element where it occurred and the maximum vorticity and the element where it occurred Chapter 3 Developing an Application 15 Hivel2D users manual The following example illustrates the model development launching and post processing of the model results using SMS SMS can be launched by double clicking the sms icon found in the computer The users are advised to read the SMS manual for installation and applications HIVEL Interface SMS version 5 0 includes a graphical
39. the downstream boundary nodes designated by BOS in the hydrodynamic flow file The next input file is run to raise the time step now that the model has settled down from startup The time step has been raised to 3 0 sec The second input file is shown in Figure D6 The final input file Figure D7 removes the tailwater constraint This run was repeated one time Figures D8 and D9 are the steady state results of the model run for water surface and velocity contours respectively These were generated by SMS There are many options available such as vectors and time series plots The results show that the bridge pier is a Appendix D Example problem 49 Hivel2D users manual choke so that the flow is subcritical in front of the pier This is apparent since the shock contour is grav 32 18900 mcon 2 20800 turb 0 1000 0 2000 time 3 0000 1 0000 step 20 20 iter 4 0 00500 bin 1 2 60 000 bin 2 2 60 000 bin 3 2 60 000 bos 2 0 14 8 6 333 334 335 336 337 338 mtyp 2 1 0 0150 2 0 0250 GRAVITY FT SEC SEC MANNING CONVERSION CB FOR VISCOSITY SMOOTH AND JUMP TIME STEP TEMPORAL DIFF TIME STEPS OUTPUT INTERVAL INUMB OF ITER CONV CRITERIA 0 000 1 3 000 0 000 1 3 000 0 000 1 3 000 NUMBER OF ELEMENT TYPES FOR ROUGHNESS Figure D6 Second hydrodynamic input file example2 flo grav 32 18900 mcon 2 20800 turb 0 1000 0 2000 time 1 0000 1 0000 step 20 20 iter 4 0 00500 bin 1 2 60 000
40. utput Files Appendix A File Formats 38 Hivel2D users manual The output data sets can be stored in ASCII files The ASCII scalar and vector data set formats are shown in Figures A6 and A7 A sample data set file is shown in Figure A8 and A9 For scalar data set files one value is listed per node For vector data set files one set of XY vector components is listed per node DATASET File type identifier OBJTYPE type Type of object data set is associated with BEGSCL Beginning of scalar data set OBJID id Object id ND numdata Number of data values NC numecells Number of elements NAME name Data set name TS istat time Time step of the following data stat 1 Status flags stat 2 stat numcells val 1 Scalar data values val 2 val numdata Repeat TS card for each time step ENDDS End of data set Figure A6 ASCII Scalar Data Set File Format DATASET Pile type identifier BEGVEC Beginning of vector dataset VECTYPE type Vector at node grid or element cell ND numdata Number of data values NC numcells Number of elements NAME name Data set name TS istat time Time step of the following data stat 1 Status flags stat 2 stat numcells vxlvyl vx2vy2 v numdata v numdata v numdata Appendix A File Formats 39 Hivel2D users manual Repeat TS card for each time step ENDDS End of data set
41. yacecakeladsahe 18 Model Ge sh ke Geeeeeee emer merry aeeter mene rete MrT ner Rey sete ye 18 Boundary COndii0ns gas dese ne ae Yn YO ees ad ae ete ees 19 M del Oi e a epee etre i erly Deets aren Nae ene eres taney Se epee R eee 21 R n Hivel TTT 22 Output TT 23 1 23 The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products Appendix A File Formats sss sss toe ee eee eee 2i HIVEL2D S per TT 21 2D Geometry HT 29 Hydrodynamic Flow lG sss 31 O tp t HES R A Geetha ee ee 38 Appendix B Boundary Conditions sese sees sese eee 41 Plow mand Out an eae Ree 4 Flow In No Flow Outset leis ae 43 No Flow In and Flow Out 2 3 a ccectncen eel nee eeccsie teense 43 No Bl yy In or A saa sage act cece el ee cas ea nee sce 44 Appendix C Troubleshooting s 45 Appendix D Example Problem 2ageciocctes ees seene 47 Appendix E Interpolation Program sss esse eee eee eee 53 Program Descriptions sssrinin ai 53 Interpolation Scheme for Quadrilateral Elements esse ee ee sees eee 54 Interpolation Scheme for Triangular Elements sss sees eee eee eters 55 CPO AU OM so oeei ces fees tenet ede tases noseta nee tenner Sa S ieg Eia 57 The contents of this report are not to be used for advertising publication or promotional purposes Citation of trade names does not constitute an official e
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