Boundary SPH for Robust Particle–Mesh Interaction in Three Dimensions

Abstract

This paper introduces an algorithm to tackle the boundary condition (BC) problem, which has long persisted in the numerical and computational treatment of smoothed particle hydrodynamics (SPH). Central to the BC problem is a need for an effective method to reconcile a numerical representation of particles with 2D or 3D geometry. We describe and evaluate an algorithmic solution—boundary SPH (BSPH)—drawn from a novel twist on the mesh-based boundary method, allowing SPH particles to interact (directly and implicitly) with either convex or concave 3D meshes. The method draws inspiration from existing works in graphics, particularly discrete signed distance fields, to determine whether particles are intersecting or submerged with mesh triangles. We evaluate the efficacy of BSPH through application to several simulation environments of varying mesh complexity, showing practical real-time implementation in Unity3D and its high-level shader language (HLSL), which we test in the parallelization of particle operations. To examine robustness, we portray slip and no-slip conditions in simulation, and we separately evaluate convex and concave meshes. To demonstrate empirical utility, we show pressure gradients as measured in simulated still water tank implementations of hydrodynamics. Our results identify that BSPH, despite producing irregular pressure values among particles close to the boundary manifolds of the meshes, successfully prevents particles from intersecting or submerging into the boundary manifold. Average FPS calculations for each simulation scenario show that the mesh boundary method can still be used effectively with simple simulation scenarios. We additionally point the reader to future works that could investigate the effect of simulation parameters and scene complexity on simulation performance, resolve abnormal pressure values along the mesh boundary, and test the method’s robustness on a wider variety of simulation environments.