Issue No.08 - Aug. (2012 vol.18)
N. Chentanez , NVIDIA PhysX Res., Bangkok, Thailand
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.86
We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation's pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver.
quadratic programming, computer graphics, differential equations, Poisson equation, QP solvers, multigrid fluid pressure solver, solid boundary conditions, linear complementarity problem, LCP, Poisson equation, Eulerian liquid simulation, pressure projection step, 3D liquid simulations, quadratic programming, Solids, Boundary conditions, Mathematical model, Multigrid methods, Equations, Linear systems, Solid modeling, physics-based animation., Multigrid, boundary condition, linear complementarity, fluid simulation
N. Chentanez, "A Multigrid Fluid Pressure Solver Handling Separating Solid Boundary Conditions", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 8, pp. 1191-1201, Aug. 2012, doi:10.1109/TVCG.2012.86