Journal of Scientific Computing

, Volume 67, Issue 2, pp 514–539 | Cite as

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



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.


Nonlinear hyperbolic conservation law Nonlinear hyperbolic balance law Shallow water magnetohydrodynamics Finite volume Entropy conservation Entropy stability 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of CologneCologneGermany

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