User Manual SmoothViz - Visualization and Computer Graphics
Contents
1. Vos sasea N J JACOBS oe UNIVERSITY HPMbviz Simulation analysis and visualization of Hamiltonian Particle Mesh method version 1 6 January 18 2012 Vladimir Molchanov Lars Linsen Contents Introduction 1 General information Mel E o ere he ee Re ee hee Be ee Hee Bes Beg Ge ee Ge ee L2 Da alormat gt 066 4k sateni ee a ee ee ee toed he Pe a User interface Tutorial What to expect next The Burgers Solution to SWE The Cosine Vortex Solution to SWE References 10 Introduction Hamiltonian Particle Mesh method HPM method was proposed by J Frank G Gottwald and S Reich 1 2 3 The authors modified ideas of Smoothed Particle Hydrodynamics SPH and Particle in Cell algorithms The new Lagrangian Eulerian method was successfully ap plied for numerical solution of Shallow Water Equations SWE which are extensively used to simulate geophysical processes HPM is a hybrid numerical method It has a natural adap tivity property like most particle methods At the same time it incorporates the procedure of artificial smoothing of the depth field over a regular grid into the classical Lagrangian formal ism Usually the inverse Helmholtz operator is applied This smoothing reduces the numerical noise and can be viewed as an efficient implementation of SPH for globally supported basis functions Many recent studies have focused on robustness accuracy and conservation properties of the HPM method It was shown2. exponential 0 or linear 1 change of the 1st parameter name string name of experiment Value of run is ignored if runseries 1 Initial conditions ic 0 constant depth ic 1 the 1D Burgers solution ic 2 the 2D cosine vortex steady solution ic 3 step function Local kernel c 0 quadratic spline c 1 cubic spline c 2 quartic spline Ilc 3 quintic spline c 4 constant c 5 linear spline splines will be re ordered in the next version Integration method im 0 Euler Ist order im 1 Runge Kutta 2nd order im 2 Runge Kutta 4th order Parameters for series of runs savel 0 global smoothing savel 1 number of grid nodes in x direction savel 2 number of grid nodes in y direction savel 3 number of grid nodes in both x and y direction savel 4 number of particles in x direction savel 5 number of particles in y direction savel 6 number of particles in both x and y direction savel 7 power of the inverse Helmholtz operator savel 8 local spline The same applies to save2 Example of parameters setting for series of runs savel 0 deltal 0 05 loop1 3 linl 1 mu 0 0 result in the global smoothing parameter change as follows u 0 0 0 05 0 1 Another example of parameters setting save2 1 delta2 2 loop2 4 lin2 0 gx 100 result in the number of the grid nodes in x direc
3. Shallow Water Equations In M Griebel and M A Schweitzer eds Meshfree Methods for Partial Differential Equations Lecture Notes in Computational Science and Engi neering Springer 26 131 142 2002 2 J Frank S Reich The Hamiltonian Particle Mesh Method for the Spherical Shallow Water Equations Atmos Sci Let 5 89 95 2004 3 C J Cotter J Frank S Reich Hamiltonian Particle Mesh Method for Two Layer Shallow Water Equations Subject to the Rigid Lid Approximation SIAM J Applied Dynamical Systems 3 69 83 2004 4 J Frank S Reich Conservation Properties of Smoothed Particle Hydrodynamics Ap plied to the Shallow Water Equations BIT 43 40 54 2003 5 V Molchanov Particle Mesh and Meshless Methods for a Class of Barotropic Fluids PhD Thesis School of Engineering and Science Jacobs University Bremen 2008 6 R Iacono Analytic Solutions to the Shallow Water Equations Phys Rev E 72 2005 7 V R Ambati O Bokhove Space time discontinuous Galerkin discretization of rotating shallow water equations J Comp Phys 225 1233 1261 2007 8 P Tassi O Bokhove C Vionnet Space discontinuous Galerkin method for shallow water ows kinetic and HLLC ux and potential vorticity generation Adv Water Res 30 998 1015 2007 10
4. als of the system dt dx dg 1 q 0 Clearly q C4 is the first integral Then gdt dx can be integrated producing gt x C2 So the general solution has the form F q qt x 0 To satisfy the initial conditions constants C and C2 should be defined A parametrization of the initial condition reads t 0 x 6 q 40 S Then C and C2 can be found from the system Ci qo S C2 Finally the solution of the Cauchy problem has the form q 0 qo 6 x q0 6 t B The Cosine Vortex Solution to SWE SWE in two spatial dimensions with topography b x y and Coriolis parameter f read ie u x y t Vu x y t ful L x y t 8V h x y t b x y 7 me u x y t Vh x y t h x y t V u x y t 8 where u u v and uf L v u A cosine vortex solution see 6 7 considered in the code is given by the following expressions h x y 2 5 cosx cosy g 9 b x y 1 0 fcosxcosy g u x y siny sinx 10 This solution is steady i e it does not depend on time t So we conclude u h 0 Then ut sinx siny 9 u Vu uuy vuy Uv vvy sinxcosy sinycosy gV h b fsinx cosysinx f siny cosxsiny Vh sinx siny u Vh sinxsiny sinysinx 0 finally V u 0 Inserting all expressions into 7 we complete the proof References 1 J Frank G Gottwald S Reich A Hamiltonian Particle Mesh Method for the Rotating
5. ing on Tab widget Functionals Show results button contains a number of checkBoxes to enable disable plots of the recorded data and change their colors and thickness of lines Data can be also read from a file by clicking on Read from file button 3 Tutorial Run the program choose Load parameters in Menu bar File choose a prm file to open Alternatively you can set up all parameters on the Lower panel and then save them clicking on Menu bar File Save parameters When avr part dist x checkBox is checked the global smoothing parameter u will be multiplied with the average particle distance in x direction i e with 2I1 nx value If Record step lineEdit value differs from the value specified in Time step lineEdit the computed quantities errors energies will be resampled using linear interpolation Click Run button to launch a single run or Run series to perform a series of runs according to parameters chosen on Tab widget Series panel A screenshot of the 3D view can be saved as a bmp file when triggering Menu bar File Screenshot 4 What to expect next Currently we gather feedbacks from interested people perform our research on optimiza tion of the HPM method and look for programming bugs in the code As soon as a relatively 7 stable state will be achieved the following features are to be available e Better manual e Streamlines and pathlines tracking e Rendering of potential vor
6. nce in x direction cnppe 0 or 1 if 1 keep constant number of particles in cell during multiple runs gx unsigned long number of grid nodes in x direction gy unsigned long number of grid nodes in y direction nx unsigned long number of particles in x direction ny unsigned long number of particles in y direction invHelm unsigned long power of the inverse Helmholtz operator global smoothing mu non negative double global smoothing length dt non negative double time step T non negative double final time g double gravity f double Coriolis parameter eps double error threshold for the Burgers solution ic 0 3 initial conditions choice lc 0 5 local kernel choice mc point wise 0 or trapezoidal 1 evaluation of particle mass im 0 2 integration method choice dt_save double time step for data recording xres unsigned long resolution in x direction yres unsigned long resolution in y direction savel int 1st parameter in multi run save2 int 2nd parameter in multi run deltal double increment of 1st parameter delta2 double increment of 2nd parameter loop1 double steps for 1st parameter loop2 double steps for 2nd parameter linl exponential 0 or linear 1 change of the Ist parameter lin2
7. se This program is distributed in the hope that it will be useful but WITHOUT ANY WAR RANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details 1 2 Data format The user can choose one of built in flows to perform a simulation These flows are known exact solutions of the Rotating SWE the boring uniform flow the Burgers solution the cosine vortex steady flow See Appendix A and B for description and discussion Alternatively one can load his her own data about initial depth profile topology values and velocity field sampled on a 2D uniform grid These data will be then interpolated two linear scheme to produce required fields sampled on particles The depth topology and velocity fields should be written into filename depth filename top and filename vel binary files correspondingly The format of files with scalar data is as follows Writing depth topology data file begin write nx number of grid nodes in x direction unsigned long write ny number of grid nodes in y direction unsigned long scalar field nx xny x double for i 1 to nx do for j 1 tony do write f i j od od end The format of file with vector data is as follows Writing velocity data file begin write nx number of grid nodes in x direction unsigned long write ny number of grid nodes in y direction unsigned long vector field n
8. that HPM equations inherit the Hamiltonian structure of SWE advect the potential vorticity properly and have better long time stability properties than SPH This was also tested in a number of numerical experiments 4 However little research has been done in the field of optimization of the method and analytical investigation of its convergence There are three characteristic scales for the system of N interacting particles in d dimensional space whose evolution is governed by HPM equations They are The artificial smoothing length u the average particle distance lpart and the mesh size A The interrelation of the scales is a subject of recent study 5 HPMv iz is a tool which serves to perform simulations using HPM method investigate the behavior of the solution with respect to the key parameters U Ipat 2 type of the kernel functions etc and visualize the results It has been and is still being developed at Visu alization and Computer Graphics Laboratory VCGL Jacobs University Bremen Germany http vcgl jacobs university de 1 General information The code is written in C Fourier transformations are performed using FFTW library We used OpenGL for 3D visualization and GLSL for the Phong shading The GUI was developed in Qt 4 7 1 1 License This program is free software you can redistribute it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the Licen
9. ticity field e More nice built in transfer functions and colors textures e Parallel implementation using OpenMP e The feature you need the most provided you send us your feedback In the current version we have disabled the functions writing the computed errors into files This option will be enabled as soon as we complete our study on optimization of HPM A The Burgers Solution to SWE As discussed in 7 the one dimensional SWE with vanishing topography Ou x t du x t _ Ah x t Ot u x t Ox gE Ox 1 Oh x t d u x t h x t Ot T Ox n a can be reduced to the inviscid Burgers equation Oq x t Oq x t _ y tat 0 3 provided u 2 gh c q x t c 3 gh c is a constant Note however that the correct form of equation 30 in 7 reads 2q x t c a h x t a e u x t eo 4 9g Substitution h and u into 1 and 2 results in Ou x t Ou x t Ah x t _ oe oe 8 2 dq x t P 2q x t c 2dq x t P 2 q x t c dq x t 3 Ot 3 3 Ox 9 Ox 2 q x t 2 Oq x t 3 ot 34 Ot and An x 1 h x t 7 a tet a x t 2 g x t c dqt gat 6 2dq x t 2g et e Zlat at _ 9g Ot 9g 3 ox 3 9g Ox 2 q x t AqQst 1 Were Oq x t _ 9g Ot 3 3 ox 8 correspondingly due to equation 3 The Cauchy problem for equation 3 dq x t Oq x t _ Ot t Ox aE 0 5 q x 0 go x 6 can be solved by characteristics method First we find integr
10. tion change as follows gx 100 200 400 800 If cnppc 1 and nx 200 the number of particles in x direction will be also changed as follows nx 200 400 800 1600 If cnppc 0 nx will remain unchanged 2 User interface Main widgets of the user interface are Menu bar on top of the main window It includes read write options and contron on the light source parameters Short information about the program and authors can be called their GL window in the center of the main window 3D view of the simulated flow and 2D plots of the computed quantities can be displayed there Slider to the left from the GL window Allows the user to change the scale of the 3D view in z direction Tab widget to the right from the GL window Show tab has a number of checkBoxes to enable disable elements on the 3D view to change their colors and to choose a proper shader Functionals tab has a set of checkBoxes to mark the quantities which should be computed during simulation recorded afterwards and shown in a new GL window after the user presses Show results button Series tab includes widgets to set parameters for a series of runs Lower panel allows to change a lot of parameters of the current simulation including name of the test gravity value Coriolis parameter grid resolution number of particles smooth ing length exponent of the smoothing operator time integration method time step final time etc Recorded data window called when click
11. x xny x3 x double for i 1 to nx do for j 1 tony do write f i j write v i j y write v i j z od od end To make your and our life easier we implemented a functions which write all parameters into a prm file read parameters from a prm file An example of such a file is put into data folder in the project The file can be modified by hand if needed since it is in a text format To load the recorded parameters either append the file name when launching the program hpmviz filename prm or choose choose Load parameters in Menu bar File The description of parameter file follows run 0 or 1 if 1 immediate launch of simulation after reading parameters run series 0 or 1 if 1 immediate launch of series of simulations after reading parame ters qkin 0 or 1 if 1 compute kinetic error qkin 0 or 1 if 1 compute kinetic error qpot 0 or 1 if 1 compute potential error qtot 0 or 1 if 1 compute total error ekin 0 or 1 if 1 compute kinetic energy epot 0 or 1 if 1 compute potential energy etot 0 or 1 if 1 compute total energy maxqkin 0 or 1 if 1 compute maximal kinetic error maxqpot 0 or 1 if 1 compute maximal potential error maxqtot 0 or 1 if 1 compute maximal total error Imomentum 0 or 1 if 1 compute linear momentum apd 0 or 1 if 1 miltiply the smoothing length with average particle dista
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