An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics
Provides a provably entropy stable numerical method for SWMHD, addressing a known bottleneck in shock-capturing simulations for geophysical and astrophysical flows.
The authors developed an entropy stable finite volume scheme for shallow water magnetohydrodynamics equations, achieving exact entropy conservation through a novel analytical flux function and a consistent source term treatment. Numerical tests confirm entropy conservation and robustness.
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.