A Fully Well-Balanced Lagrange--Projection-Type Scheme for the Shallow-Water Equations

Abstract

This work focuses on the numerical approximation of the shallow water equations using a Lagrange--projection-type approach. We propose a fully well-balanced explicit and positive scheme using relevant reconstruction operators. By fully well-balanced, it is meant that the scheme is able to preserve stationary smooth solutions of the model with nonzero velocity, including of course also the well-known lake at rest equilibrium. Numerous numerical experiments illustrate the good behavior of the scheme.