Numerical approximation of the shallow water equations with Coriolis source term

Emmanuel Audusse (1) , Virgile Dubos (2) , Arnaud Duran (3, 4) , Noémie Gaveau (5) , Youssouf Nasseri (6) , Yohan Penel (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 ICJ - Institut Camille Jordan
4 MMCS - Modélisation mathématique, calcul scientifique
5 IDP - Institut Denis Poisson
6 I2M - Institut de Mathématiques de Marseille

We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Emmanuel Audusse, Virgile Dubos, Arnaud Duran, Noémie Gaveau, Youssouf Nasseri, et al.. Numerical approximation of the shallow water equations with Coriolis source term. ESAIM: Proceedings, 2021, 70, pp.31-44. ⟨10.1051/proc/202107003⟩. ⟨hal-03182659v2⟩