User Manual Adaptive Multi-Resolution Wavelet
Contents
1. The elliptic solver can be used either to solve general elliptic problems of the type Cu f or as a part of initial condiitons where a linear system of PDEs is solved during each grid iteration instead of prescribing u analytically The adaptive grid refinement procedure provides a way to obtain the solution initial conditions on an optimal compressed grid The pseudocode for both the iterative global elliptic solver and the time evolution problem are shown below User Manual initial guess m 0 uy and GY while m 0 or m gt 1 and G2 4 G27 or f7 Lu oo gt 6 m m 1 perform forward wavelet transform for each component of uj forall levels 7 J 1 1 create a mask M for dj gt end extend the mask M with adjacent wavelets perform the reconstruction check procedure construct G27 wa interpolate uj to GZ end if solve Lu f using Local Multilevel Elliptic Solver end Algorithm 1 Global Elliptic Solver initial conditions n 0 ug and G while tn lt tmax bagi HAt integrate the system of equations using Krylov time integration to obtain uj perform forward wavelet transform for each component of upt for all levels 7 J 1 1 create a mask M for di gt end extend the mask M with adjacent wavelets perform the reconstruction check procedure construct G2 if g Age interpolate uy to g end if n n 1 end Algorithm 2 Time Evolution Solver Modeling2. Simulation and Visualization Environment 2 2 Code Categories and Files The code consists of FORTRAN and Matlab files The FORTRAN code saves results in terms of active wavelet coefficients while Matlab files are set up to read output files from the FORTRAN code perform an inverse wavelet transform and visualize the results The FORTRAN files can be divided into the followqing categories Case Files user _case f90 user _input inp where the user_case is the name of a specific case set up by user that can be located in any directory while user_input in the user defined input file Note that the same case can have multiple input files Core Files wlt_3d_main f90 wavelet _3d f90 wavelet_filters f90 elliptic_solve_3d f90 time_int_cn f90 time_int_krylov_3d f90 This category inculdes all the core files for the Adaptive wavelet collocation method We don t need to modify any part of these files Data Structure files wavelet_3d_wrk f90 wavelet_3d_wrk_vars f90 Shared Variables Files shared_modules f90 wavelet_3d_vars f90 elliptic_solve_3d_vars f90 wavelet_filters_vars f90 io_3d_vars f90 This category includes all the variable only modules 7 e these modules contain no functions or subroutines User Manual Supplementary Utility Files input _files_reader f90 read_init f90 read_data_wray f90 io_3d f90 util_3d f90 default _util f90 vector_util f90 endienness_big f90 endienness_small f90 reverse
3. The j_range is the range of resolution that MATLAB will use to plot your solution The bounds argument determines the domain that will be plotted The figure is set to plot the solution using a contour plot If you would like to see the grid you must set the figure type to grid The plot_comp variable is the component of the solution that you want to plot This is defined in the channel_compressible f90 code The station number is which output step you are plotting In this case it is set to 100 which is the final output time for this case 4 2 More Data Visualization Res2Vis A tool is available to transform AWCM code result files into VTK PLOT3D or CGNS formats for further visualization with ParaView VisIt Tecplot or similar software To compile the tool specify the database type and the case name as usual the compilation target will be vis instead of wlt_3d The tool will be found in the test case executable directory e g in TestCases CASE_NAME under some generic name res2vis_DATABASE_CASE out Type res2vis for the complete manual In short at least two file names have to be provided to the tool the AWCM result file name and the base name for the output file A VTK unstructured mesh binary output file will be generated by adding vtk suffix to the 11 User Manual provided base output name An optional flag p will produce PLOT3D binary output by using xyz and q suffixes Use optional flag c to generate CGNS file It
4. 8 6 FUNCTION Laplace_diag This is where the diagonal term used in the Laplace equation definition is made A function similar to c_diff_fast yet only gives the diagonal terms is c_diff_diag 5 8 7 FUNCTION Laplace_rhs This is where f in equationB can be defined Since f is already defined in user_initial_condtions is passed directly to Linsolve and is not required anywhere else in the code it does not need to be here 5 38 8 SUBROUTINE user_read_input No parameters are read from the input file for this example 5 3 9 SUBROUTINE user_scales The default scales are used for this case 5 4 CaseFile inp Details Elliptic Solver All of the paramters are set up in the same way as the previous example except that t_end 0 This prevents the time integration from beginning and outputs only the final solution to the elliptic problem in the results subdirectory The output file will end in 0000 res since it is the first output file of problem 25 User Manual 6 Creating Your Own Cases Before moving forward grabbing a test case the looks similar to what you want to do and modifying it to suit your needs it would be better to create your own directory outside of the source code where you will not be editing files under subversion management There are a couple reasons for this One is that whenever an update is available you won t have a conflict with the new incoming version and the second is that if you make a mistake somewhere you
5. It should be noted that there are multiple ways in which the IC file can be formatted and you must specify its format beforehand with IC_file_fmt You also must be sure to specify how the output will be formatted binary or ascii The unformatted binary version works much faster and takes up less disk space so that is the recommended method The domain size is specified with coord_min and coord_max We have specified three different dimensions in the case that dimension is set to 3 then the input file is ready to use In the case of our 2 D run it simply ignores the extra dimension In order to avoid problems at the boundaries it is sometimes necessary to specify a coord_zone_min and coord_zone_max The way these parameters work is that if you pick a coord_zone parameter to be inside of the domain all points on the finest level of resolution will be included between that coordinate and the boundary The max portion corresponds to the upper side of the domain and the min portion corresponds to the lower side The overall solution error is controlled with the parameter e The code has been set up to allow the use of two different s depending on your particular situation Eps_init can be used as a separate initial thresholding parameter for eps_adapt_steps number of steps before using the regular eps_run parameter In our case there is no difference between the two Setting a threshold parameter is only effective on its own if all integrated va
6. are performed by the scripts from TestCases util directory RUN sh RUN_2 sh and RUN_3 sh The first script RUN sh performs compilation of various targets for different data bases and test cases Cartesian product of list of targets list_ta list of data bases list_db and list of test cases list_ca All three lists are defined inside the file RUN_lists txt which is sourced from all RUN sh scripts The major output of the first test is inside the file TestCases TEST_LOGS COMPILE log It contains minimum information regarding successful compilation of test cases The second test performed by RUN_2 sh script examines execution and restart capabil ities of the code The major output can be found inside the file TestCases TEST_LOGS RUN log and inside the files TEST REPORT in test case directories The control parameters for the second test for each test case can be found in test case subdirectory test_in in the file local_test_parameters txt Input files will be generated according to the provided rules in the same test case subdirectory test_in in the file rules inp Examine the mentioned files for details The third test is performed by RUN_3 sh script It examines code execution for differ ent combinations of input parameters Instead of predefined during the second test inputs the third test generates inputs by itself Input generator uses numerous_input_rules_parameters txt 29 User Manual file from the test case subdirectory test
7. names similar to all other compilers 33 User Manual References Goldstein D E amp Vasilyev O V 2004 Stochastic coherent adaptive large eddy simulation method Phys Fluids 16 7 2497 2513 34
8. reading of that input parameter by the main code the public function of module INPUT_FILE_READER has to be called from the main code REAL var here the value of ParName to be stored CALL input_real ParName var KEY SOME COMMENT where KEY takes the value stop or default The first one terminates the code execution if the parameter ParName is not present in the input file while the second one let the code continue running as if nothing happened The last argument of the function is an optional string comment If the reading is performed in verbose mode the screen output of the function call is the following ParName 1 234e 5 SOME COMMENT For details examine the code for the general input reader which is located in the mod ule INPUT_FILE_READER file input_files_reader f90 The module contains several private parameters which might need to be changed depending on the system and or compiler 31 User Manual 9 2 Result File Format res An endian independent I O library is used to read or write result files The library consists of two files tree c io h and tree c io cc The header file io h contains short description of the functions to use from Fortran subroutines to read or write result files The header file also contains definitions of integer and real types which could be changed on the systems with nonstandard C integer or real sizes Additionally file io 3d f90 contains some private parameter
9. technique a diagonal term needs to be created from our DRHS The diagonal term for both the Navier Stokes and the Euler equations are shown in the example Note that this is only for the Crank Nicolson method When using the Krylov integrator this section does not need to be defined because it is not used 5 1 14 SUBROUTINE user_project This routine is mostly used for incompressible flows where the pressure needs to be tracked but not integrated The Crank Nicolson method is used with this projection step to ensure that the velocity vector v remains divergent free The small_vortex_array case demon strates this feature more clearly 5 1 15 FUNCTION user_chi If there is to be an obstacle in the flow using Brinkman penalization you would determine your x function here If it is equal to 1 0 it is inside the boundary and if it is equal to zero then it is outside 5 1 16 SUBROUTINE user_stats After results of a new time step are available you may want to generate some statistics based on those results This function serves that purpose and is called from the main code User_stats allows you to make these calculations without touching the main code 6 1 17 SUBROUTINE user_cal_force If an obstacle has been defined in the user_chi function the lift and drag are calculated here 5 1 18 SUBROUTINE user_readinput In the subroutine setup_pde we defined our variables Re Pra gamma alpha T_top and U_wall This is where we read them int
10. BROUTINE user_initial_conditions If you know the analytical initial condition it is set up here 5 1 5 SUBROUTINE user_algebaic_BC Algebraic boundary conditions are set by solving the general equation L f 1 There are three main subroutines used to solve this equation The first is user_algebaic_BC This subroutine sets up the u portion of the equation As you can see from this example Dirichlet conditions are created for both the velocity and energy on the top and bottom boundaries The top wall temperature is T_top and the bottom wall is 1 0 17 User Manual 5 1 6 SUBROUTINE user_algebaic_BC_diag Since the equation above is solved iteratively the diagonal terms of L need to be provided user_algebaic_BC_diag becomes this term In this case for Dirichlet conditions they are equal to 1 5 1 7 SUBROUTINE user_algebaic_BC_rhs To finish setting up the equations that need to be solved user_algebaic_BC_rhs is the right hand side of the above equation f In this case the right hand side is zero 5 1 8 FUNCTION Laplace This is the elliptic solver portion of the code It is not used in this case but is demonstrated in Secion 5 3 5 1 9 FUNCTION Laplace_diag This is where the diagonal term used in the Laplace equation definition is made An example of its use is provided in Secion 6 3 5 1 10 FUNCTION Laplace_rhs This is where f in equation BJis defined An example of its use is provided in Secion E3 5 1 11 FUNCT
11. FORTRAN code that is compiled in the source directory Casename inp will contain any variables that are not hard coded into the 90 file The casename f90 file contains all the subroutines you see below followed by a brief description of what they do There are two modules that are needed for memory and variable allocation specific to your case and the rest are functions or subroutines Modules Module Name Description user_case db Module created for database memory allocation This is stored in casename PARAMS 90 user_case This is the actual case module that contains all of the functions and subroutines that are used in this file It is located in casename f90 Subroutines Subroutine Name Description user_setup_pde Sets up the number of variables that are inte grated or interpolated on the initial time step and any subsequent step user_exact_soln Stores the exact solution in memory user_initial_conditions Defines the initial conditions if they can be deter mined analytically user_algebraic_BC Sets conditions on boundaries 14 user_algebaic_BC_rhs user_project Laplace Laplace_diag Laplace_rhs user_rhs user_Drhs user_Drhs_diag user_chi user_stats user_cal_force user_read_input user_additional_vars user_scalar_vars user_scales user_cal_cfl Modeling Simulation and Visualization Environment Specifies the right hand side for boundary conditions Used for Crank Nicolson time inte
12. ION user_rhs In the function user_rhs we need to supply the right hand side of the main governing equation The left hand side is the time derivative that we re integrating and the right hand side is everything else This is supplied to the function user_rhs As you can see the right hand side has already been set up for both the Euler and Navier Stokes equations In this test case it will be using the full Navier Stokes equations because the logical variable NS is true as described above For details on how to use the derivative operator c_diff_fast see Section 5 3 5 1 12 FUNCTION user_Drhs Since the Crank Nicolson and Krylov are implicit iterative time integration solvers we need to provide a first order perturbation to help the iterative solver converge more quickly The user provides this perturbation to the main code through the function user_Drhs Since the right hand side has already been defined finding the perturbation is simply a matter of applying the linearized theory In this case the linearized equations are given as an example for both the Navier Stokes and Euler equations If there is a mistake made when entering the 18 Modeling Simulation and Visualization Environment equations into DRHS it may still converge but it may take a few more iterations Otherwise the solver will continue to iterate without reaching its error threshold criteria indefinitely 6 1 18 FUNCTION user_Drhs_diag When using the Crank Nicolson
13. User Manual Adaptive Multi Resolution Wavelet Based Modeling Simulation and Visualization Environment Code Structure and Setup alpha release May 8 2007 Modeling Simulation and Visualization Environment 1 Introduction Welcome to the world of numerical modeling using the computationally efficient dynamically adaptive Adaptive Wavelet Collocation Method AWCM The numerical algorithm used in this method is a finite difference based scheme which uses an adaptive wavelet transform in conjunction with a prescribed error threshold parameter to determine which grid points are needed in the solution By reducing the number of points needed to solve the numerical solution the computational cost is significantly reduced resulting in large data compression It has been shown that the error within the solution using this technique is bounded by Ce where C is usually around 10 warning Citation donoho 1992 on page 1 undefined The error threshold parameter is prescribed beforehand and is used throughout the entire simulation It is recommended that the equations be non dimensionalized for the numerical algorithm even though L and Ly normalization techniques are used to further scale the equations Typical values for the error threshold parameter range from 10 to 1071 anything below that range usually decreases the compuational efficiency significantly and anything above that range has significant error that isn t
14. _endian f90 Supplementary FFT Package Files fft 90 fftpacktvms f90 fft interface temperton f90 fft_util f90 spectra f90 ch_resolution_fs f90 These supplementary files are located in subdirectory FFT and if necessary can be used for extracting statistics in homogeneous directions Supplementary LINPACK files dimach f derfc f derf f dgamma f dgeev f dgels f dqage f dqag f dtrsm f dum f fort 1 gaussq f needblas f rlmach f zgetrf f zgetri f Modeling Simulation and Visualization Environment Visualization Files c_wlt_3d m c_wlt_3d_movie m c_wlt_inter f90 inter3d m mycolorbar m mycontourf m c_wlt_3d_isostats m vor_pal m These are used to visualize the output results All these files are contained in subdirectory post_process User Manual 3 Getting Started 3 1 Obtaining the Source Code Currently the most efficient means of obtaining the code is through the use of Subversion The use of Subversion allows you to keep your code up to date with the current release with out starting all over again Subversion is available for download at http subversion tigris org and documentation is available at http svnbook red bean com Once you have subversion installed make a directory where you want to put the source code directory called wlt_3d Move into this directory and use the command svn checkout https www cora nwra com svn wlt branches NASA You will be asked for a login name and pas
15. _in to produce input files with all the combinations of given parameters within a predefined range Examine the mentioned file for details The major output of the third test can be found inside the file TestCases TEST_LOGS RUN_numerous log It should be noted that some of the parameters from the file local_test_parameters txt used by the second test are also to be used by the third test Additionally scripts com pare_results sh and compare_dbs sh contain internal debug variables LDBG_CMPRES and LDBG_CMPDBS Set them to unity for some additional output during the tests or for the debugging the test suite itself 8 2 Tests for the post processing tools Various tests for the post processing tools and subroutines are performed by scripts in test_in subdirectories inside post_process directory The first post processing test resides in post_process view_spectra adaptive test_in directory It tests turbulent statistics using Fourier transform on adaptive grid which is cur rently limited to 3D periodic cases The test could be run from post_process view_spectra directory as sh adaptive test_in RUN sh or gmake tests Test s major results to be found inside the file post_process view_spectra adaptive TEST_LOGS RUN log The second post processing test resides in post_process visualization test_in di rectory It tests res2vis visualization tool and could be run from the directory visualization as sh test_in RUN sh or gmake tests The second te
16. always have a working copy that you can return to for reference It is recommended that you create another sister directory next to the main source directory where you will put your new cases When compiling you can still use relative paths or you can use absolute paths which ever you prefer You will also have to make sure that you edit the path for showme3D m to reference the correct directory as well 26 Modeling Simulation and Visualization Environment 7 NASA Specific Modules There have been five new modules created specifically for NASA s purposes They are located in TestCases dns They are organized into two different files dns_module f 90 and urans_module f90 dns_module f90 simulates flow around a cylinder with the flow moving from left to right at Ma 0 2 using the compressible Navier Stokes equations and an acoustic Reynolds number of Re 1000 urans_modeule f90 solves the same problem but uses the k w turbulence model The model is incorporated in the user_case module in the user_rhs user_Drhs subroutines Since it is using the Krylov solver user_Drhs_diag is not specified In this case the Reynolds number is Re 10 Both of these cases use the Freund Boundary method to prevent reflections from occuring at the domain walls Both of these files include the additional modules needed by the main case file that uses them except for the far field acoustics predictor FWH which is located in the source directory There are a t
17. at level of resolution will be used on the contour to calculate the far field acoustics This parameter must always be smaller than the finest level of resolution 7 4 DNS and uRANS These two modules are basically implemented in the two different dns_module f90 and urans_module f90 FORTRAN files Both are set up for fluid flow using the Navier Stokes equations The only difference between them is that the uRANS file uses the k w model in the user_rhs user_Drhs and user_Drhs_diag subroutines 28 Modeling Simulation and Visualization Environment 8 Code Development A test suite is available for code developers The structure of the test suite is the following make tests from the source main directory will execute a the tests for the test cases b the tests for the post processing tools and subroutines Complete testing may take up to several hours depending on your system and test input parameters 8 1 Tests for the test cases All the tests for the test cases could also be run from TestCases directory as cd TestCases gmake tests It is also possible to start different tests separately as cd TestCases gmake testl gmake test2 gmake test3 The detailed description can be found in TestCases README and TestCases util README files The files in directories TestCases test_in contain control parameters affecting the execution of the testing scripts for each test case Examine the files for details In short tests for the test cases
18. d is initially not in thermal equilibrium with the walls The domain is periodic in the x direction with Dirchlet conditions on the top and bottom boundaries 5 1 1 MODULE user_case This is the main module that the entire case file is built into Any variables that you want to be available globally throughout the entire module should be defined in this section Below where it says case specific variables the variable n_var_pressure is declared As of now this parameter must always be declared because the code is set up to solve both compressible and incompressible flows Following are some non dimensional parameters Re Pra gamma and alpha as well as boundary condition parameters T_top and U_wall As you will see these variables are imported from the test_in base inp file in the user_read_input sub routine There are also two other logical parameters that are defined to set up the equations and how they are solved NS and NSdiag NS switches the equations from Navier Stokes to Euler equations TRUE for Navier Stokes and FALSE for Euler equations At this point a hyperbolic solver capable of resolving shocks with the hyperbolic Euler equations has been developed but is not implemented yet It should become available with further updates NSdiag should be set to true if NS is true and you are using the Crank Nicolson time inte grator If the Krylov integrator is used the user_Drhs_diag subroutine is never called and doesn t need to be tr
19. e both VTK and plot3D ASCII files out vtk out q out xyz and the data will be filtered by applying the threshold 0 15 to the variable number 4 of the result file res2vis res in 0 6 3 t 12 Modeling Simulation and Visualization Environment writes data as VTK files in 0000 vtk in 0003 vtk in 0006 vtk into the current directory for each of the input file from the directory res in 0000 res in 0003 res in 0006 res 13 User Manual 5 Case Files This section will attempt to provide some familiarization with the more intricate details of setting up your own case The code is equipped with some test cases that can be used as a reference for setting up a new case Each test case has a set of subroutines that must be present in order for the code to function properly If one of the functions does not apply in your case it must remain present but you can leave the contents other than variable definitions blank For example if you are using periodic boundary conditions you can leave the details in the user_algebaic_BC function blank but do not delete the function itself Each case should have its own separate directory with its own case files and results output directory Three case files are needed for each case casename f90 and casename inp and casename PARAMS 90 where casename is the name of the particular case your are running e g case_elliptic_poisson or case_small_vortex_array Casename f90 will be the actual
20. easily ignored The wavelets used in the wavelet transform can be of any even order of accuracy Each wavelet s accuracy is determined by its stencil size which is typically prescribed in terms of the number of points used on each side of the point being calculated Two stages are used to calculate the wavelet coefficients a predict stage and an update stage The number of points used on each side in the predict stage are called n_predict and the number used during the update stage are called n_update In order to ensure the wavelet properties are maintained these two parameters should be equal Similarly the stencil size for derivative calculations is prescribed in the same way Since the wavelets support is naturally centered the default setting for derivative calculations is centered as well The stencil size for a centered derivative calculation is 2 n_diff where n_diff is the number of points on each side of the location being calculated In practice all three of these parameters are normally the same to achieve the highest performance and accuracy THE AWCM is set up to solve two main types of partial differential equations PDEs elliptic and time evolving or a combination of the two The elliptic solver can be used to solve for the initial condition used in a time evolving problem or can be used solely on its own The time evolving portion can also be supplied with an analytical initial condition and uses either a Krylov or Crank Nicolson
21. ed 0 and n_var_adapt 1 n_integrated 1 to TRUE The 0 index indicates adaptation when setting up the initial condition and 1 index adapting at each time step afterwards We also need the grid to interpolate all of the integrated variables as time moves along as well Adaptation means that the grid will evolve based upon a given variable Interpolation is what needs to happen in order to add a previous time step to the next In this case it is not necessary to interpolate the pressure so we have set the first 4 variables to be interpolated both at the initial condition and all time steps thereafter We want to save all 5 variables at each write step so we have set n_var_save as true for all variables n_var For the time being please ignore the time level counters and leave them the way they are These will most likely be phased out in the future An exact solution exists for this problem so n_var_exact_soln has been set to true If you find that you need more points due to a a certain variable you can create a scaleCoeff lt 1 0 to add more points to that variable If it is left as 1 0 it will scale the solution in its default manner according to your error threshold parameter e 5 1 8 SUBROUTINE user_exact_soln This is where we calculate the exact solution Even though it is called u it is not the same u that is used to numerically calculate the solution The main code takes this u and stores it as the exact solution somewhere else 5 1 4 SU
22. f resolution remains constant throughout the domain hence the grid is called uniform 21 User Manual The parameters i_h and i_1 specify the order in which boundaries are stored in the u array and what type of boundary conditions will be imposed either algebraic or evolutionary The order of the wavelets used are specified with N_predict and N_update These parame ters determine how many points are used on either side of the point being interpolated In our case they are 2 so we are using 4th order wavelets N_diff is the number of points used on each side of a centered difference scheme to calculate the derivatives Since N_diff is 2 we are using a 4th order central differencing scheme Generally it is wise to make all three of these parameters the same The next two parameters IJ_ADJ and ADJ_type deal with the fine details of how the code chooses to pick points It s generally good to leave IJ_ADJ as 1 for all three levels If ADJ_type is set to 0 it will use less points and run faster but if convergence becomes an issue set this parameter to more conservative This alone may solve a convergence issue when faced with one If non periodic boundary conditions are used BNDzone should normally be set to true It will use the parameters coord_zone_min and coord_zone_max when this is on BCtype specifies the type of boundary conditions used if custom ones are not needed The time integration method chosen in this example to be the implicit Kry
23. for storing the data As of now the main database in use is db_wrk but db_tree and db_lines will be available soon The next argument is which case you are going to run Since the compilation is done from the source directory the path to the case file needs to be specified and the executable will be placed in that directory The path can be specified as an absolute path or relative to the source directory Before attempting to compile anything a makefile must be created specific to your com puter Under the source directory is a subdirectory called makefiles machine_specific 8 Modeling Simulation and Visualization Environment Inside this directory are numerous different makefiles all in the form makefile some_name The makefile in the source directory references the makefiles in this directory through the use of an environment variable WLT_COMPILE_HOSTNAME You will need to create an environment variable called WLT_COMPILE_HOSTNAME and set it equal to your some_name You will also need to copy one of the makefiles in the makefiles machine_specific directory that is similar to your computer s configuration and rename the file makefile some_name Make sure to make any changes necessary to the names of the compiler and flags so that it will work on your machine Once all this is done gmake will know what to do when you compile 3 3 Elliptic Solver Example There are several test cases provided with the code and are located in the TestCases d
24. gest as cfl_out 5 2 CaseFile inp Details Channel Compressible The input file is where all of the variables that are not hard coded into your case file are stored As seen in the previous section any variables you need are read using an input_real or input_integer statement For the channel_compressible case we ran a 2 D Navier Stokes simulation Inside of the test_in base inp file you will see all of the parameters that are needed to run this case The first several variables pertain to input output and initialization parameters file_gen is whatever you want the output in the results subdirectory to be saved as There are three main ways to initialize your initial conditions The first way is to use an analytical solution which you provide in the user_initial_conditions subroutine Another way is to restart a previous run from a given output time In order to do this you simply specify the name of the file name for IC_filename set IC_restart T and specify the output time to start with with IC_restart_station A third way is to use some other file for the initial conditions which may or may not match the current configuration of your case You can take the input 20 Modeling Simulation and Visualization Environment data and manipulate it to match your current case and then start your simulation In order to start with this configuration you would make sure IC_restart F set IC_from_file T and specify the IC_filename as in the restart case
25. gration to get projections of variables that are needed for inte gration but not actually integrated with the ac tual solver Sets up the Laplacian Sets up the diagonal terms for the Laplacian Sets the right hand side for the Laplacian Sets the right hand side of the PDE being solved Sets the Jacobian of the right hand side of the PDE Sets up the diagonal terms for the Jacobian when the Crank Nicolson time integration method is used This is your boundary used for immersed flow boundary conditions Any user specified statistics that need to be calcu lated to analyze new data can be calculated here Used to calculate lift and drag on any bodies in the flow Not implemented yet Any user defined variables defined in the case name inp file are read through this subroutine Where any additional variables are calculated Any scalar non field parameters that need to be calculated can be done here Used to override the default scales routine Override default cfl condition and use user created condition 15 User Manual 5 1 CaseFile f 90 Details Channel Compressible Now that we ve taken a general look at how the case files are structured let s look at a specific case and explain how it is set up The channel_compressible f90 case is set up to solve the Navier Stokes Equations in a channel which is initially at rest with an upper wall moving at a velocity of 0 1 and the bottom wall is at rest The flui
26. heavy side functions and the boundary will be specified with the user_chi function in the user_case module 7 2 Freund Boundary The Freund s buffer zone is used to avoid the spurious reflections from the domain walls It basically works by accelerating the flow to supersonic speeds near the boundaries by adding volumic terms to the governing equations In order to activate this feature you simply set 27 User Manual the logical flag Freund_active located in the dns_module inp and urans_module files to TRUE 7 3 FWH This module is used to predict the far field acoustics As of now it is only available in 2 D but 3 D will be available in the future In order to use this module there is a logical flag inside of the input file additional_nodes_active If the prediction is needed set it to TRUE When the module is activated you must create a seperate directory inside of the results directory called filegen which is the base name of your output files specified in your input file The additional far field prediction files will be stored in that subdirectory In addition the patches used to predict the far field acoustics must be specified in the input file as well The number of patches used is specified by n_additional_patches and the locations of the points used to create the n point polygon are specified with the x_patches and y_patches parameters The final paramter that must be specified is j_additional_nodes This paramter determines wh
27. iler has to be informed not to attach underscores to the function names 9 8 2 IBM Power4 AIX zlc alf A typical machine specific file is makefile regatta msi umn edu In addition to providing a correct library for linking C and Fortran functions and dealing with underscores a special flag DDATABASE_INTERFACE_LOWERCASE might need to be used The purpose of that flag is to include tree c lowercase h which forces all C functions into lowercase It might need to be used to overcome some compilation problems with xlf compilers 32 Modeling Simulation and Visualization Environment 9 3 8 PC WinXP MSVC MSVF First known problem is the failure of MS to recognize C99 standard As a consequence there are no standard integer types stdint h it means that the endian independent library may require some adjustments on such systems Examine the files tree c io h and io_3d f90 for details Currently we are using MSC_VER macro which is defined by MS compilers to provide MS specific definitions Another known problem is that Fortran GETARG func tion require module DFLIB which we currently include through the mentioned MSC_VER macro The extensions of files tree c cc might need to be changed to cxx Inside MS Visual Studio function calling convention might need to be changed to _ cdecl and Fortran string length has to be passed after all the arguments Additionally some care has to be taken of capitalizing and attaching underscores to the function
28. implicit time integrator Due to the fact that the time integrators are implicit algorithms the only time constraining parameter used in the code is the CFL condition As long as CFL lt 1 the time integrator should function properly and the solution will remain within the anticipated error margin The grid used with the AWCM can be described as if it had two parts a base grid to build upon and several further levels of refinement The level of resolution at any point in time is described by the variable j_lev For any simulation minimum j_min and maximum j_max 1 User Manual levels of resolution must be specified The base grid size is prescribed with the M_vector variable Combining all of these parameters will give a grid with a minimum and maximum grid sizing For example if a 2 D simulation is to be performed using a domain of dimension 2 0 x 1 0 with periodic boundary conditions in the y direction and the aspect ratio is desired to be unity the following could be a suitable grid setup dimension 2 Myector 8 4 0 periodic 0 1 0 jmin 2 lance l This sets the dimensionality of the simulation to a 2 D simulation so that the third index in the M_vector and periodic vector are ignored The base grid of 8 x 4 is on the j_lev 1 level but because the solution is not periodic in the x direction the base grid is really 9 x 4 However the minimum level of resolution is set to be 2 so the coarsest grid possible in this simulatio
29. in the post_process directory 10 Modeling Simulation and Visualization Environment 4 Data Visualization Once you have compiled and run your test case and compiled the post processing executable c_wlt_inter 90 discussed in Section B 4 you are ready to view your results files saved in the results subdirectory There are a few ways to visualize your results now In the past MATLAB has been the primary data visualization tool Over the past year or two new visualization tools have been under development which are capable of 3 D volume rendering and will be introduced in the following subsections 4 1 MATLAB Visualization Tools In order to view the output files using MATLAB you must return to the case directory Once you are in the case directory open the file showme3D m Make sure to edit the post_process directory to its correct location on your computer Once this is done you are ready to visually view the output using MATLAB Executing showme3D within the MATLAB command window should read the data from the specified file within showme3D m If you look at the showme3D m file further you will notice down near the bottom all of the arguments used to call the plotting function c_w1lt_3d are briefly explained At the bottom a call to this function is shown with each argument defined for you The first argument in this list is the file name channel_compressible_test You will find this matches the name in the channel_compressible inp file
30. irec tory In order to demonstrate how to successfully compile the code we will start with the EllipticTestl From the source directory if you move into the TestCases EllipticTest1 directory and list the files you will see the following list of files along with some others that aren t of importance case_elliptic_poisson f90 case_elliptic_poisson PARAMS f90 results directory testin showme3D m From looking at the different files one can conclude that the case name is case_elliptic_poisson As of now the exact syntax used to compile is gmake DB databaseName CASE path of case caseName wlt_3d Remember that this is always done in the source directory For our example path of case is TestCases EllipticTest1 the case name is case_elliptic_poisson and we ll be using the database db_wrk The following syntax should successfully compile the code gmake DB db_wrk CASE TestCases EllipticTest1 case_elliptic_poisson wlt_3d Make sure to add the target wlt_3d at the end so the compiler will know what to do Once the code has finished compiling the executable will be located in the case directory and will be called in this example wlt_3d_db_wrk_case_elliptic_poisson out If we move to the case directory the case can be executed by running the executable and specifying which input file is to be used as an argument The input files are located in the test_in subdirectory For example if we wanted to run the 2 D test problem we would use the fo
31. llowing command User Manual wlt_3d_db_wrk_case_elliptic_poisson out test_in base inp It should be noted at this time that during the compilation step an important file was overlooked which is the case_elliptic_poisson PARAMS f90 file Inside this file are two parameters needed by the database in order to construct the databases size and dimensions If this file is absent the compiler will fail However a run time error can occur if the parameters are not set large enough to handle the input file s dimensions and number of variables being stored Inside this file the parameter max_dim is set to 3 This allows the database to allocate enough room to run both the 2D and 3D input files The number of variables is also set to 10 n_var_db 10 which is large enough to handle the 3D case with some extra variables stored For the 2D case it would be possible to change max_dim to 2 for increased performance but it is set to 3 for now so that both cases can be run without changing this file 3 4 Post Processing Once you have succesfully run the test case from within the test case directory the output files will be stored in the results subdirectory The output files have the file extension res In order to view the output files in MATLAB the post process file c_wlt_inter f90 needs to be compiled From the source directory compile all the needed files with the target inter using the command gmake DB db_wrk inter The executable created is located
32. lov scheme It can also use an implicit Crank Nicolson technique The next several variables all involve temporal aspects of the code The beginning and ending of the simulation are specified with t_begin and t_end The initial time step used to start off the run is dt The minimum and maximum time steps are set with dtmax and dtmin Dtmin can serve as a stability indicator in that many times the time step will become smaller and smaller as the solution begins to diverge If dt drops below dtmin it is usually because there is a problem dtwrite specifies the time interval used for writing output to the ouput files An additional feature has been recently added to the code which allows you to force the solution to be written after every time step This is done by creating a file named filegen force_write in the case directory where filegen is the basename for your output files created in the results directory After each time step the main executable checks for the existence of this file If the file exists it will write the output from the time step that was just executed otherwise it will wait until the next t_write corresponding to the specified dtwrite The parameter t_adapt can be used to make all time steps below t_adapt of the same size and once t is greater than t_adapt the time step is free to change with the solution The maximum and minimum cfl conditions are set with cflmax and cflmin The minimum cfl serves as a trigger for stopping the ti
33. me integrator in the case that the solution is diverging In the channel_compressible case example we need to define several paramters They are set here for no reason in particular Note that the order in which variables are declared is not important The variable Zero_Mean is for cases in which you want the mean value of the first 1 dim 22 Modeling Simulation and Visualization Environment variables to remain zero The next several variables are for the Krylov time integrator and the elliptic solver It is best not to touch these unless you have a good understanding of how it works and are having problems with the way the current paramters are set up If you wish to insert an object into the flow using Brinkman Penalization you would set the obstacle variable to T Its location size and movement directions can all be specified using the various different variables You would probably create a few of your own variables and then make sure to define that objects domain in the user_chi subroutine The rest of the variables are other integration parameters that should normally be left alone 5 3 CaseFile f90 Details Elliptic Solver Another important functionality of the code is the ability to efficiently solve elliptic prob lems The previous example focused on the time integration portion and this example will focus on how to solve an elliptic problem There is a test case set up in the directory TestCases EllipticTest1 with a case name ca
34. n will be Myector2 periodic 17 8 corresponding to a grid spacing h 2 16 1 8 0 125 and a total of 136 points Similarly the finest grid possible in this simulation will be Myector2 periodic 513 256 corresponding to a grid spacing of h 2 512 1 256 3 9 x 107 and a total of 131328 points Throughout the solution the resolution will change such that the finer levels of resolution will be used in the regions where localized structures are present If the simulation only uses 10 000 points it would only be using 7 6 of the points available and have a compression ratio of 13 1 The rest of this manual will try to familiarize you with the codes organization and how a user can create their own simulations A brief overview of the codes organization will be given in Section BJand point out which files need to be modified and others that should be left untouched Section B will demonstrate how to obtain the code using subversion set up a makefile compile and run the code Section 4 will show how to compile and use the post processing tools for data visualization Finally Section will proceed with the details of the case files how they are used and how to customize them to any particular situation Modeling Simulation and Visualization Environment 2 Code Structure 2 1 Overall Code Organization The Adaptive wavelet collocation method AWCM solver consists of two parts 1 elliptic solver and 2 time evolution solver
35. o the module from the test_in base inp input file Each variable is read in separately with its own input_real command The input_real command is only used to input real type numbers If you want to read an integer you would use input_integer The parameter stop tells the code that if that variable is not read 19 User Manual properly it will stop the code execution If you look in the test_in base inp file you can see how to set up your own variables just like these 5 1 19 SUBROUTINE user_additional_vars Any additional variables that aren t integrated but are stored in the main storage array u are calculated here In our case we are storing pressure in the n_var_pressure portion of u that we created in setup_pde Again normally it would be better to calculate pressure in the post processing step but we are storing it here as an example 5 1 20 SUBROUTINE user_scalar vars If there are any scalar non field parameters defined at the beginning of the module that need to be calculated they should be handled here 5 1 21 SUBROUTINE user_scales In the situation that you wish to override the default scales routine in the main code you would do that here 6 1 22 SUBROUTINE user_cal_cfi If you wish to override the default cfl condition you would do that here The subroutine get_all_local_h returns the grid spacing for all points on the active grid We then deter mine the cfl for each grid point and ultimately select the lar
36. otoal of five new modules Brinkman_penalization Freund_boundary wlt_FWH DNS and uRANS They are explained in the following sections 7 1 Brinkman Penalization This module is used to deal with the complex obstacles inside the flow field It uses Brinkman Penalization to add semi porous obstacles into the flow field which act as solid bodies to appropriately divert the flow Inside of both dns_module f90 and urans_module f90 you will find the boundary is defined in two different sections First it is defined in the Brinkman_obstacle subroutine inside the Brinkman_penalization module and also in the initial_obstacle subroutine inside the user_case module These two subroutines serve very different functions initial_obstacle serves as a function that the grid can adapt to since in the initial conditions all the flow variables are constant Brinkman_obstacle defines the obstacle that is used by the Brinkman_penalization module to add the penalization terms to the fluxes calculated in user_rhs user_Drhs etc The module is activated by the flag Brinkman_active located in the dns_module inp file It uses one parameter nita which determines the porosity of the obstacle The variable nita should be a small value approximately 0 01 or smaller to ensure that the obstacle is close to being a full solid As of now the obstacles cannot be fully discontinuous heavy side functions Instead hyperbolic tangeants are used In the future it will be possible to use
37. riables are normalized to the same scale This is usually not the case and a scaling method Scale_Meth needs to be specified to keep the relative error in check In our channel_compressible case all the equations are normalized with a mean value of zero so choosing Linf error as the scaling method is not a bad choice However in other situations it may be better to use an L2 norm error or possibly a RMS scaling method In some situations the time scales can change very rapidly which causes your scales to rapidly vary as well Since this can sometimes be problematic a temporal filter has been provided to slow the speed at which these scales change scl_fltwt This parameter has the range of 0 1 where zero corresponds to no filtering and 1 corresponds to being completely based upon historical scales In every simulation the minimum and maximum grid size needs to be specified by set ting the minimum and maximum levels of resolution J_MN and J_MX as well as the initial M_vector In our case the M_vector is 4 4 and J_MN and J_MX are 2 and 4 The minimum grid size is M_vector 2 J_MN prd 17x16 and the maximum grid size is M_vector 2 J_MX 65x64 In our case J_MX is set relatively small because it is a test case and we want to limit the level of resolution for computational reasons The boundaries are set to be periodic in the x directiona and has Dirchlet conditions in the y direction Although our grid is adaptive the grid spacing on each level o
38. s which could be changed on systems with nonstandard Fortran integer or real sizes In order to simplify the code development it is recommended to keep all I O operations with result files inside READ SOLUTION and SAVE SOLUTION subroutines of the module IO 3D file io 3d f90 Providing version control and backward compatibility for all the future result file formats will be easier in this case In short if you need to read result file e g for some post processing call READ_SOLUTION If you would like to save data in res format call SAVE_SOLUTION Current version of the code is capable of reading old endian dependent res files so called 01 31 2007 format as well as new so called 02 01 2007 endian independent format res files without interaction with user Unless specifically requested only new endian independent format is used to save the result files 9 3 Porting the Code Some notes have to be made regarding portability of the code to different platforms First of all for all the platforms some additional libraries may need to be installed to fully utilize capabilities of the code e g HDF CGNS or LAPACK libraries 98 1 PC Linuz gcc icc ifort A typical machine specific file is makefile scales colorado edu Problems might occur with C and Fortran linking A correct library has to be provided as LINKLIB It can be something like usr lib libstde so 5 or similar depending on the system compiler Additionally Fortran comp
39. se_elliptic_poisson f90 The following subsections will discuss how the elliptic test case is configured 5 3 1 MODULE user_case As in the previous example this is the main module that the entire case file is built into Any variables that you want to be available globally throughout the entire module should be defined in this section You can see that since we are solving Poisson s equation the number of variables stored in the database is n_var_db 1 The number of possible dimensions max_dim is set to 3 to allow all possible configurations 5 3 2 SUBROUTINE user_setup_pde Again in this routine we set the global parameters the main code uses to know how many equations it is integrating interpolating saving and how many variables there is an exact solution for For this case the number of variables being integrated is 1 there are no addi tional variables being stored and we do have an exact solution to compare with No pressure needs to be stored because the time evolution part of the code is not being used 5 8 8 SUBROUTINE user_exact_soln There is an exact solution to this problem which is defined in this routine 5 3 4 SUBROUTINE user_initial_conditions When the elliptic solver is used the user_initial_conditions subroutine functions as the main place to set up the problem The elliptic solver uses the subroutine Linsolve to solve 23 User Manual the general equation Lu f 2 In this case the right hand side f is set
40. should be noted that ParaView has no problems with reading VTK unstructured mesh files The same is true for Tecplot reading CGNS files As for the ancient PLOT3D format Tecplot will auto detect file structure for ASCII files only For binary files file structure has to be specified manually as Plot3D Function Unstructured not Multi Grid Moreover Tecplot known to have problems with reading binary 3 dimensional plot3D files on some architectures so use ASCII plot3D or which seems to be a better solution CGNS format 4 2 1 complete manual of res2vis Usage res2vis OPTIONS IN_FILE OUT_FILE res2vis OPTIONS IN_DIR IN_FILE OUT_DIR STATION_BEGIN STATION_END STEP Data options t apply inverse wavelet transform to show the data values wavelet coefficients are displayed by default i use integer space coordinates according to the mesh coordinates are real by default Output formats v VTK file default p plot3D files CGNS file Additional output formats a VTK plot3D the output file is ASCII binary by default E VTK CGNS use tetrahedra blocks will be written by default Additional filtering before the transform e threshold_value number_of_variable_for_threshold l maximum_level_to_use Files input_result_file output_filename input_directory generic_input_filename output_directory first_station last_station step Example res2vis vpa e 0 15 4 res input 0001 res out produc
41. st major results to be found inside the file post_process visualization TEST_LOGS RUN log The third post processing test resides in post_process interpolation test_in di rectory The test is performed by RUN sh script It tests the subroutines related to the interpolation to a random coordinate location The major test output to be found as usual inside the file post_process interpolation TEST_LOGS RUN log 30 Modeling Simulation and Visualization Environment 9 Appendix 9 1 Input Parameter File Format inp A general input file format has been used for inp files to provide the code with the required input parameters Each inp ASCII file normally contains a header with short format specifications tS a ass a aaa gt General input file format comments start with till the end of the line string constant are quoted by or boolean can be T F 1 0 on off in or without or quotes integers are integers real numbers are whatever e g 1 1 0 1e 23 1 123d 54 vector elements are separated by commas spaces between tokens are not important empty or comment lines are not important order of lines is not important Pos SS RSS SSS RSS SSS SRS SS SRE SSS RS Se a a Se Sees SSeS eae To provide the code with a real parameter Par Name 1 234 10 the following line should be inserted into the input file ParName 1 234e 5 Some comments if required To allow the
42. sword you should have this information already Enter the information and the import will commence It is important that you do not modify any of the files in the main source code If you do the next time a newly released version of the code will conflict with the changes you have made It is important that you create your own case files and edit those exclusively so that you do not introduce any conflicts If you do find a bug in the main source code please send an email to oleg vasilyev colorado edul so that the problem is properly resolved If these guidelines are followed each time an updated version is released When an update does become available you can see what files have been changed before hand by running the command svn status q from the source directory The q option suppresses output associated with files that are not under version control Then to proceed with updating the changed files run the command svn update and you will have the latest release If after updating to the latest release there are problems and your code will not run anymore you can perform and svn revert and the code will be restored to its previous version 3 2 Compilation and Execution The source code is always compiled from the source directory regardless of which case file executable you are creating There are three arguments that must be passed to gmake in order for it to know what to do First of all the compiler needs to know which database to use
43. to ouput the first order derivative to and the second order derivative respectively The next variable is jlev which is the current level the solution is on nlocal is the number of points being used and stored in u per variable Another important variable is the method meth meth1 and meth2 Youll notice for the simpler second derivative case meth 0 where as for the divergence of the gradient method methi 2 and meth2 4 are used This is so that one sided differencing can occur For example meth 2 corresponds to backwards in space differencing whereas meth 4 corresponds to forwards in space differencing Another important parameter is the parameter that follows meth This can be either 10 01 or 11 It is simply a logical indicator as to which derivative is to be computed where the first and second indices correspond to the first order and second order derivatives respectively Next comes ne_local which is just the number of variables stored in the array u The next parameter is set to 1 in this case but this value corresponds to which variable stored in u you want to differentiate It can be a single value or it can be a list of values say 1 n_var This is better demonstrated in user_rhs of Section B I At the bottom of this subroutine the boundary values are specified for all of the different types of boundary conditions In this case they re all specified to be Dirichlet conditions 24 Modeling Simulation and Visualization Environment 5
44. ue 5 1 2 SUBROUTINE user_setup_pde In this routine we set the global parameters the main code uses to know how many equations it is integrating interpolating saving and how many variables there is an exact solution for The number of variables that are integrated n_integrated is set to dim 2 since we are solv ing for p pe and the momentum equations in dim dimensions In the test_in base inp file the dimsion parameter is set to dim 2 Leave n_time_levels and n_var_time_levels as they are They will soon be phased out Any additional variables that are not inte grated but you want calculated at each time step set as n_var_additional As an example n_var_additional is set to 1 so that we can calculate the pressure and save it at each time step This is totally unnecessary as pressure can be calculated during the post processing step but it is performed here purely for demonstration purposes The next step is to fill in the variable names according to how we arrange our variables 16 Modeling Simulation and Visualization Environment We will fill in the variables depending upon how many dimensions there are starting with density as the first variable x momentum as the second and so on The grid does not need to adapt to all 5 variables Pressure the 5 variable is simply found using the 4 conserved variables Obviously we will only need the grid to adapt to the 4 conserved variables so we set n_var_adapt to n_var_adapt 1 n_integrat
45. up and passed directly to the subroutine Linsolve In other cases f can be defined using the Laplace_rhs function The other functions that are passed in Linsolve are Laplace and Laplace_diag These functions will be defined in the following sections Once Linsolve has completed its iterations the solution will be printed to an output file and the code will stop 5 3 5 FUNCTION Laplace This is the elliptic solver portion of the code This is run before any time evolution ever begins It is created to solve equation P The Laplace subroutine sets up the operator on the left hand side of this relation It is important to note that the boundary conditions for the elliptic solver are specified within this function and the next two following In this case we are setting up the Laplacian as the operator Two seperate techniques are set up to calculate the Laplacian One way is to simply take the second order derivative in dim dimensions or the other is to take the divergence of the gradient It switches between the two with the parameter divgrad which is set to false in this case so the default is the simpler second order derivative The derivatives are calculated with the function c_diff_fast The syntax used in this subroutine is as follows CALL c_diff_fast u du d2u jlev nlocal meth 01 ne_local 1 ne_local Youll notice that the first three arguments are u du and d2u corresponding to the function that is being differentiated the variable
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