Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2025

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

Résumé

We analyse a class of energy-stable and linearly well-balanced numerical schemes dedicated to the nonlinear Shallow Water equations with Coriolis force. The proposed algorithms rely on colocated finite-difference approx- imations 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. Among the proposed algorithms a colocated finite-volume scheme is described. Numerical results show a very clear improvement around the nonlinear geostrophic equilibrium when compared to those of classic Godunov-type schemes.
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Dates et versions

hal-03509990 , version 1 (04-01-2022)
hal-03509990 , version 2 (29-07-2023)
hal-03509990 , version 3 (10-02-2025)

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Citer

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. SIAM Journal on Scientific Computing, 2025, 47 (01), pp.A1-A23. ⟨10.1137/22M1515707⟩. ⟨hal-03509990v3⟩
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