Energy stable and linearly well-balanced numerical schemes for the non-linear Shallow Water equations with Coriolis force

Emmanuel Audusse (1) , Virgile Dubos (2) , Noémie Gaveau (3) , Yohan Penel (4)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LHSV - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics
3 IDP - Institut Denis Poisson
4 ANGE - Numerical Analysis, Geophysics and Ecology

This work is dedicated to the analysis of a class of energy stable and linearly well-balanced numerical schemes dedicated to the non-linear Shallow Water equations with Coriolis force. The proposed algorithms rely on colocated finite volume approximations formulated on cartesian geometries. They involve appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic equilibrium. We show that the resulting methods ensure semi-discrete energy estimates and numerical results show a very clear improvement around the nonlinear geostrophic equilibrium when compared to those of classic Godunov-type schemes.

Domains: Numerical Analysis [math.NA]

Emmanuel Audusse, Virgile Dubos, Noémie Gaveau, Yohan Penel. Energy stable and linearly well-balanced numerical schemes for the non-linear Shallow Water equations with Coriolis force. 2023. ⟨hal-03509990v2⟩