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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