Accurate Boundary Condition for Moving Least Squares Material Point Method using Augmented Grid Points

Abstract

This paper introduces an accurate boundary-handling method for the moving least squares (MLS) material point method (MPM), which is a popular scheme for robustly simulating deformable objects and fluids using a hybrid of particle and grid representations coupled via MLS interpolation. Despite its versatility with different materials, traditional MPM suffers from undesirable artifacts around wall boundaries, for example, particles pass through the walls and accumulate. To address these issues, we present a technique inspired by a line handler for MLS-based image manipulation. Specifically, we augment the grid by adding points along the wall boundary to numerically compute the integration of the MLS weight. These additional points act as background grid points, improving the accuracy of the MLS interpolation around the boundary, albeit with a marginal increase in computational cost. In particular, our technique makes the velocity perpendicular to the wall nearly zero, preventing particles from passing through the wall. We compare the boundary behavior of 2D simulation against that of naïve approach.