ENERGY-STABLE AND LINEARLY WELL-BALANCED NUMERICAL SCHEMES FOR THE NONLINEAR SHALLOW WATER EQUATIONS WITH THE CORIOLIS FORCE

We analyze a class of energy-stable and linearly well-balanced numerical schemes dedicated to the nonlinear shallow water equations with the Coriolis force. The proposed algorithms rely on colocated finite-difference 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 semidiscrete 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.