Particle-Laden Fluid on Flow Maps

TL;DR

This paper introduces a new particle flow map framework for simulating particle-laden fluids, accurately modeling viscosity and drag, and enabling high-fidelity visualizations of complex flow phenomena.

Contribution

It presents a coupling mechanism for physical and virtual particles using a Poisson system and a path integral formula to incorporate dissipative forces into flow map simulations.

Findings

Accurately simulates vortex bulbs and viscous tails.

Captures hierarchical structures and fractal branching.

Demonstrates realistic phenomena like drop breakup and coalescence.

Abstract

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures.