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An entropy stable finite volume scheme for the equations of shallow water magnetohydrodynamics
Mathematical Institute, University of Cologne, Cologne, Germany.ORCID iD: 0000-0002-5902-1522
Mathematical Institute, University of Cologne, Cologne, Germany.
2016 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 67, no 2, p. 514-539Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 67, no 2, p. 514-539
Keywords [en]
Nonlinear Hyperbolic Conservation Law, Nonlinear Hyperbolic Balance Law, Shallow Water Magnetohydrodynamics, Finite Volume, Entropy Conservation, Entropy Stability
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156865DOI: 10.1007/s10915-015-0092-6ISI: 000374414500006Scopus ID: 2-s2.0-84940530681OAI: oai:DiVA.org:liu-156865DiVA, id: diva2:1315788
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-24Bibliographically approved

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