We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle‐based fluid simulation) in three‐dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one‐way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow‐band using the Closest Point Method. In this way, we efficiently compute high‐resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline.

中文翻译：

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移动 3D 表面上的高效 2D 模拟

我们提出了一种方法来模拟演化表面上的流体流动，例如水面上的油膜。给定三维空间中的动画表面（例如，从基于粒子的流体模拟中提取），我们在此基础动画上添加第二个模拟。通常，我们在从动画输入表面获得的水平集表面上求解偏微分方程 (PDE)。输入表面的属性被传输到一个稀疏体数据结构，然后用于模拟。我们将输入属性的单向耦合策略引入到我们的模拟中，并且我们将质量和动量守恒添加到使用最近点方法解决窄带 PDE 的现有方法中。通过这种方式，我们可以在粗糙的输入表面上有效地计算高分辨率 2D 模拟。