Efficient 2D Simulation on Moving 3D Surfaces

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.