MLS pressure boundaries for divergence-free and viscous SPH fluids

Abstract

In this paper we present 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 three previous techniques. One previous technique mirrors the pressure from fluid to boundary particles. Another one extrapolates the pressure from fluid to boundary particles, but uses a gradient that is computed with Smoothed Particle Hydrodynamics (SPH). The third one solves a pressure Poisson equation (PPE) for boundary particles. In our experiments, we indicate artifacts in the three previous approaches. We show that these artifacts are significantly reduced with our approach resulting in simulation steps that can be twice as large. We motivate that gradient-based extrapolation is more accurate than mirroring. We further motivate that, due to particle deficiency at the boundary, the SPH gradient is error prone. This is less the case for our proposed MLS gradient. Moreover, our approach is computationally less expensive as solving a PPE for the boundary particles. We present challenging and complex scenarios to illustrate the capabilities of our method. In addition, we demonstrate that the proposed boundary handling is applicable to highly viscous fluids.