Particle-Laden Fluid on Flow Maps

We propose a novel framework for simulating ink as a particle-laden flowusing particle flow maps. Our method addresses the limitations of existingflow-map techniques, which struggle with dissipative forces like viscosityand drag, thereby extending the application scope from solving the Eulerequations to solving the Navier-Stokes equations with accurate viscosity andladen-particle treatment. Our key contribution lies in a coupling mechanismfor two particle systems, coupling physical sediment particles and virtualflow-map particles on a background grid by solving a Poisson system. Weimplemented a novel path integral formula to incorporate viscosity and dragforces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by thebulging and breakup of suspension drop tails, torus formation, torus disinte-gration, and the coalescence of sedimenting drops. In particular, our methoddelivered high-fidelity ink diffusion simulations by accurately capturingvortex bulbs, viscous tails, fractal branching, and hierarchical structures.