Tiled Characteristic Maps for Tracking Detailed Liquid Surfaces

Abstract

We introduce tiled characteristic maps for level set method that accurately preserves both thin sheets and sharp edges over a long period of time. Instead of resorting to high-order differential schemes, we utilize the characteristics mapping method to minimize numerical diffusion induced by advection. We find that although a single characteristic map could be used to better preserve detailed geometry, it suffers from frequent global re-initialization due to the strong distortions that are locally generated. We show that when multiple localized tiled characteristic maps are used, this limitation is constrained only within tiles; enabling long-term preservation of detailed structures where little distortion is observed. When applied to liquid simulation, we demonstrate that at a reasonably amount of added computational cost, our method retains small-scale high-fidelity (e.g., splashes and waves) that is quickly smeared out or deleted with purely grid-based or particle level set methods.