Efficient 2D Simulation on Moving 3D Surfaces

TL;DR

This paper introduces an efficient method for simulating fluid flow on evolving 3D surfaces by solving PDEs on level set surfaces, enabling high-resolution 2D simulations on coarse animated surfaces for visual effects.

Contribution

It presents a novel approach combining level set PDE solving with sparse volume data transfer, including conservation laws and one-way coupling, to improve simulation efficiency on moving surfaces.

Findings

Enables high-resolution 2D fluid simulations on coarse, animated 3D surfaces.

Integrates conservation of mass and momentum into PDE-based surface simulations.

Facilitates workflow integration for visual effects creators.

Abstract

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.