Primal SPH Solver for Strongly Coupled Multiphase Simulations with High Density Ratios

Abstract

In recent years, the Smoothed Particle Hydrodynamics (SPH) approach has been increasingly used for multiphase simulations involving interactions between diverse materials. A critical component of an SPH simulator is the pressure solver, which not only facilitates the simulation of compressible or incompressible fluids but also handles contact by preventing penetration between different materials. Currently, most SPH simulations in computer graphics employ implicit dual pressure solvers such as PBF, IISPH, or DFSPH. However, these solvers often exhibit instability when simulating high density ratios. Furthermore, they are difficult to strongly couple with many existing methods for non‐pressure forces, which typically utilize primal formulations. Consequently, pressure and non‐pressure solvers are often only weakly coupled, which can lead to stability issues. We present a novel implicit primal SPH pressure solver designed for multiphase simulations. Our method enables stable simulation of multiple interacting materials with large density ratios. We show that our solver robustly handles ratios of up to 1:1000 (e.g., air‐water interactions) which was not possible with previous implicit SPH pressure solvers. Moreover, we demonstrate how our solver allows for strong coupling with existing implicit simulation methods for viscosity, elasticity, and surface tension. Overall, our strong coupling significantly improves stability in complex multiphase simulations involving fluids, highly viscous materials, and deformable solids.