Semi-implicit two-speed Well-Balanced relaxation scheme for Ripa model

Emmanuel Franck (1, 2) , Laurent Navoret (2, 1)

1 IRMA - Institut de Recherche Mathématique Avancée
2 TONUS - TOkamaks and NUmerical Simulations

In this paper, we propose a semi-implicit well-balanced scheme for the Ripa model based on a two-speed relaxation. The method both preserves equilibria and has an implicit step that reduces to the inversion of a constant Laplacian. Numerical simulations show that the scheme well capture low-Froude flows.

Mots clés: relaxation method; shallow-water model; semi-implicit scheme

Domaines: Analyse numérique [math.NA]

Emmanuel Franck, Laurent Navoret. Semi-implicit two-speed Well-Balanced relaxation scheme for Ripa model. FVCA 2020, Jun 2020, Bergen, Norway. pp 735-743, ⟨10.1007/978-3-030-43651-3_70⟩. ⟨hal-02407820⟩