Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations

Abstract

We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed firstand secondorder schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states. AMS subject classifications: 76M12, 65M08, 35L65, 86-08, 86A05