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.

中文翻译：

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流图上的含颗粒流体


我们提出了一种新的框架，用于使用粒子流图将墨水模拟为充满粒子的流动。我们的方法解决了现有流图技术的局限性，这些技术与粘度和阻力等耗散力作斗争，从而将应用范围从求解欧拉方程扩展到求解具有精确粘度和负载粒子处理的纳维-斯托克斯方程。我们的主要贡献在于两个粒子系统的耦合机制，通过求解泊松系统，将物理沉积物粒子和虚拟流图粒子耦合在背景网格上。我们实现了一种新的路径积分公式，将粘度和阻力纳入粒子流图过程。我们的方法可以对各种充满颗粒的流动现象进行最先进的模拟，例如悬浮液滴尾部的膨胀和破裂、圆环形成、圆环分解和沉淀液滴的聚结。特别是，我们的方法通过准确捕获涡流球、粘性尾巴、分形分支和分层结构，提供了高保真油墨扩散模拟。