The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-404

“Advanced Liquid Simulation Techniques for Computer Graphics Applications”

by Youngmin Kwak

August 2010

The particle level set method (PLSM) and the lattice Boltzmann method (LBM) have been two major physics-based liquid simulation techniques used in computer graphics to generate splendid and dynamic visual effects. The PLSM suffers from a high computational cost, which arises from the global pressure correction step whereas the LBM requires a large memory size to store distribution functions.

In this research, we propose a hybrid lattice Boltzmann method (HLBM), which integrates the PLSM and the LBM, to visualize realistic liquid motion with emphasis on the behavior of the liquid-gas interface. The HLBM first runs the LBM solver, computes macroscopic velocities, and extrapolates the velocity field to the gas region. Subsequently, the level set function and particlesare advected by the extrapolated velocity field, and advected particles are used to correct errors in the level set function based on the PLSM. Finally, the density difference between the LBM and the PLSM solvers is added to distribution functions to correct errors of the LBM. Simulation results show that the HLBM improves the quality of the fluid simulation without increasing the number of grids. As compared with the simulation using the LBM with 50^3 grids, the mean of the geometrical distance from the ground truth has been decreased by 21.70% and 13.02% for the water drop and the broken dam simulations, respectively, using the HLBM with the same number of grids. The simulation results also show that the HLBM offers more splashy and dynamic visual effects than the LBM without increasing the grid size.

Also we propose a multicomponent-multiphase hybrid lattice Boltzmann method (MCMP-HLBM) which integrates the PLSM and the MCMP-LBM, to visualize realistic bubble motion with emphasis on the behavior of the liquid-bubble interface. The MCMP-HLBM first runs the MCMP-LBM solver and computes composite macroscopic velocities. Then, the level set function and particles are advected by the the composite velocity field, and advected particles are used to correct errors in the level set function based on the PLSM. Finally, the density difference between the MCMP-LBM and the PLSM solvers is added to the distribution functions to correct the errors of the MCMPLBM. We test the method for the bubble coalescence and rising simulations. The results show that the MCMP-HLBM improves the quality of the fluid simulation without increasing the number of grids. Compared with the simulation using the MCMP-LBM, the normalized absolute difference from the ground truth is 61.50% and 36.50% less using the MCMP-HLBM for two dimensional two- and three-bubble coalescence simulations, respectively, using the MCMP-HLBM with the same number of grids. Also the normalized absolute difference from the ground truth using the MCMP-LBM has been decreased by 44.93%, 56.02%, and 40.62% for two dimensional single-, two-, and three-bubble rising simulations, respectively, using the MCMP-HLBM with the same number of grids. For the case of three dimensional single-, two-, and three-bubble rising simulations using the MCMP-HLBM, the mean of the geometrical distance from the ground truth has been decreased by 11.75%, 38.95%, and 26.57% as compared with the simulation using the MCMP-LBM, respectively. The simulation results also show that the MCMP-HLBM offers more detailed visual results than the MCMP-LBM without increasing the grid size.

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