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In this work, we design an entropy stable, finite volume approximation forthe shallow water magnetohydrodynamics (SWMHD) equations. The method is novelas we design an affordable analytical expression of the numerical interfaceflux function that exactly preserves the entropy, which is also the totalenergy for the SWMHD equations. To guarantee the discrete conservation ofentropy requires a special treatment of a consistent source term for the SWMHDequations. With the goal of solving problems that may develop shocks, wedetermine a dissipation term to guarantee entropy stability for the numericalscheme. Numerical tests are performed to demonstrate the theoretical findingsof entropy conservation and robustness.

An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics