Dispersion Kernels for Water Wave Simulation

摘要

We propose a method to simulate the rich, scale-dependent dynamicsrnof water waves. Our method preserves the dispersion propertiesrnof real waves, yet it supports interactions with obstacles and isrncomputationally efficient. Fundamentally, it computes wave accelerationsrnby way of applying a dispersion kernel as a spatially variantrnfilter, which we are able to compute efficiently using two core technicalrncontributions. First, we design novel, accurate, and compactrnpyramid kernels which compensate for low-frequency truncationrnerrors. Second, we design a shadowed convolution operation thatrnefficiently accounts for obstacle interactions by modulating the applicationrnof the dispersion kernel. We demonstrate a wide range ofrnbehaviors, which include capillary waves, gravity waves, and interactionsrnwith static and dynamic obstacles, all from within a singlernsimulation.