Solving General ShallowWave Equations on Surfaces

Abstract

We propose a new framework for solving General Shallow Wave Equations (GSWE) in order to efficiently simulate water flows on solid surfaces under shallow wave assumptions. Within this framework, we develop implicit schemes for solving the external forces applied to water, including gravity and surface tension. We also present a two-way coupling method to model interactions between fluid and floating rigid objects. Water flows in this system can be simulated not only on planar surfaces by using regular grids, but also on curved surfaces directly without surface parametrization. The experiments show that our system is fast, stable, physically sound, and straightforward to implement on both CPUs and GPUs. It is capable of simulating a variety of water effects including: shallow waves, water drops, rivulets, capillary events and fluid/floating rigid body coupling. Because the system is fast, we can also achieve real-time water drop control and shape design.