MLS Pressure Extrapolation for the Boundary Handling in Divergence-Free SPH

Abstract

We propose a novel method to predict pressure values at boundary particles in incompressible divergence-free SPH simulations (DFSPH). Our approach employs Moving Least Squares (MLS) to predict the pressure at boundary particles. Therefore, MLS computes hyperplanes that approximate the pressure field at the interface between fluid and boundary particles. We compare this approach with two previous techniques. One previous technique mirrors the pressure from fluid to boundary particles. The other one extrapolates the pressure from fluid to boundary particles, but uses a gradient that is computed with Smoothed Particle Hydrodynamics (SPH). We motivate that gradient-based extrapolation is more accurate than mirroring. We further motivate that our proposed MLS gradient is less error prone than the SPH gradient at the boundary. In our experiments, we indicate artifacts in previous approaches. We show that these artifacts are significantly reduced with our approach resulting in simulation steps that can be twice as large compared to previous methods. We further present challenging and complex scenarios to illustrate the capabilities of the proposed boundary handling.