A Fast and Compact Solver for the Shallow Water Equations

Abstract

This paper presents a fast and simple method for solving the shallow water equations. The water velocity and height variables are collocated on a uniform grid and a novel, unified scheme is used to advect all quantities together. Furthermore, we treat the fluid as weakly compressible to avoid solving a pressure Poisson equation. We sacrifice accuracy and unconditional stability for speed, but we show that our algorithm is sufficiently stable and fast enough for real-time applications.