We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

中文翻译：

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薄膜平滑粒子流体动力学流体

我们提出了一种基于粒子的方法来模拟薄膜流体，该方法共同促进了侵蚀性的表面变形和剧烈的切向流动。我们从表面张力驱动的Navier-Stokes方程建立动力学模型，并使用渐近润滑理论降低了维数，并基于弱可压缩的平滑粒子流体动力学（SPH）定制了一组微分算子，用于演化的点集表面。关键的见解是，SPH的可压缩性质（在其典型用法中不利）有助于我们共同开发厚度，计算表面张力并在薄膜上增强流体不可压缩性。通过这种方式，我们能够以基于物理的方式将表面变形与平面内流动双向耦合。我们可以模拟复杂的涡旋漩涡，通过提供真实的视觉结果和数值验证，由瑞利-泰勒（Rayleigh-Taylor）不稳定性，毛细波，牛顿干涉条纹和Marangoni效应对表面自由变形造成的指弹效应。我们系统的基于粒子的特性还使其能够方便地处理拓扑结构变化和余维转换，从而使我们能够将薄膜模拟与各种3D现象结合起来，例如夹住不稳定的链状体，在重力作用下滴落，液滴合并以及气泡破裂。