Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 67, Issue 2, Pages 514-539Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-015-0092-6
Keywords
Nonlinear hyperbolic conservation law; Nonlinear hyperbolic balance law; Shallow water magnetohydrodynamics; Finite volume; Entropy conservation; Entropy stability
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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.
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