An implicitly stable mixture model for dynamic multi-fluid simulations.

Abstract

Particle-based simulations have become increasingly popular in real-time applications due to their efficiency and adaptability, especially for generating highly dynamic fluid effects. However, the swift and stable simulation of interactions among distinct fluids continues to pose challenges for current mixture model techniques. When using a single-mixture flow field to represent all fluid phases, numerical discontinuities in phase fields can result in significant losses of dynamic effects and unstable conservation of mass and momentum. To tackle these issues, we present an advanced implicit mixture model for smoothed particle hydrodynamics. Instead of relying on an explicit mixture field for all dynamic computations and phase transfers between particles, our approach calculates phase momentum sources from the mixture model to derive explicit and continuous velocity phase fields. We then implicitly obtain the mixture field using a phase-mixture momentum-mapping mechanism that ensures conservation of incompressibility, mass, and momentum. In addition, we propose a mixture viscosity model and establish viscous effects between the mixture and individual fluid phases to avoid instability under extreme inertia conditions. Through a series of experiments, we show that, compared to existing mixture models, our method effectively improves dynamic effects while reducing critical instability factors. This makes our approach especially well-suited for long-duration, efficiency-oriented virtual reality scenarios.