  In this work, we design an entropy stable, finite volume approximation for
the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel
as we design an affordable analytical expression of the numerical interface
flux function that exactly preserves the entropy, which is also the total
energy for the SWMHD equations. To guarantee the discrete conservation of
entropy requires a special treatment of a consistent source term for the SWMHD
equations. With the goal of solving problems that may develop shocks, we
determine a dissipation term to guarantee entropy stability for the numerical
scheme. Numerical tests are performed to demonstrate the theoretical findings
of entropy conservation and robustness.
