A Moving Least Square Reproducing Kernel Particle Method for Unified Multiphase Continuum Simulation

Xiao-Song Chen, Chen-Feng Li, Geng-Chen Cao, Yun-Tao Jiang and Shi-Min Hu

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square Reproducing Kernel Method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MLS) has also been used in computer graphics to estimate d formation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework,including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc.

A Moving Least Square Reproducing Kernel Particle Method for Unified Multiphase Continuum Simulation