MPM simulation of interacting fluids and solids.

The material point method (MPM) has attracted increasing attention from the graphics community, as it combines the strengths of both particle- and grid-based solvers. Like the smoothed particle hydrodynamics (SPH) scheme, MPM uses particles to discretize the simulation domain and represent the fundamental unknowns. This makes it insensitive to geometric and topological changes, and readily parallelizable on a GPU. Like grid-based solvers, MPM uses a background mesh for calculating spatial derivatives, providing more accurate and more stable results than a purely particle-based scheme. MPM has been very successful in simulating both fluid flow and solid deformation, but less so in dealing with multiple fluids and solids, where the dynamic fluid-solid interaction poses a major challenge. To address this shortcoming of MPM, we propose a new set of mathematical and computational schemes which enable efficient and robust fluid-solid interaction within the MPM framework. These versatile schemes support simulation of both multiphase flow and fully-coupled solid-fluid systems. A series of examples is presented to demonstrate their capabilities and performance in the presence of various interacting fluids and solids, including multiphase flow, fluid-solid interaction, and dissolution.