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.

翻译：我们提出了一种利用颗粒流图模拟墨水作为颗粒悬浮流体的新框架。该方法解决了现有流图技术在处理粘性和阻力等耗散力方面的局限性，从而将应用范围从求解欧拉方程扩展到求解具有精确粘性及悬浮颗粒处理的纳维-斯托克斯方程。我们的核心贡献在于提出了一种双颗粒系统的耦合机制：通过求解泊松系统，在背景网格上耦合物理沉积颗粒与虚拟流图颗粒。我们实现了一种新颖的路径积分公式，将粘性力和阻力纳入颗粒流图过程。该方法能够对各种颗粒悬浮流动现象进行前沿模拟，包括悬浮液滴尾部的膨胀与断裂、环形结构形成、环形结构解体以及沉降液滴的聚并过程。特别地，本方法通过精确捕捉涡旋球体、粘性尾迹、分形分支和层级结构，实现了高保真度的墨水扩散模拟。