Tiled Characteristic Maps for Tracking Detailed Liquid Surfaces

Abstract

AbstractWe 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.