A second-order well-balanced scheme for the shallow-water equations with topography

Christophe Berthon (1) , Raphaël Loubère (2, 3) , Victor Michel-Dansac (4)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 CNRS - Centre National de la Recherche Scientifique
3 IMB - Institut de Mathématiques de Bordeaux
4 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the well-balanced numerical scheme for the shallow-water equations with topography introduced in [8] and its second-order well-balanced extension, which requires two heuristic parameters. The goal of the present contribution is to derive a parameter-free second-order well-balanced scheme. To that end, we consider a convex combination between the well-balanced scheme and a second-order scheme. We then prove that a relevant choice of the parameter of this convex combination ensures that the resulting scheme is both second-order accurate and well-balanced. Afterwards, we perform several numerical experiments, in order to illustrate both the second-order accuracy and the well-balance property of this numerical scheme. Finally, we outline some perspectives in a short conclusion.

Domaines: Analyse numérique [math.NA]

Christophe Berthon, Raphaël Loubère, Victor Michel-Dansac. A second-order well-balanced scheme for the shallow-water equations with topography. HYP2016, Aug 2016, Aachen, Germany. ⟨hal-01513186⟩