A Multigrid Fluid Pressure Solver Handling Separating Solid Boundary Conditions

• Published in: IEEE transactions on visualization and computer graphics Vol. 18; no. 8; pp. 1191 - 1201
• Main Authors: Chentanez, N., Mueller-Fischer, Matthias
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2012; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; boundary condition; Boundary conditions; Computer simulation; Equations; fluid simulation; Handles; linear complementarity; Linear systems; Liquid crystal polymers; Liquids; Mathematical model; Multigrid; Multigrid methods; physics-based animation; Poisson equation; Quadratic programming; Solid modeling; Solids; Solvers; Studies
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 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.