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Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
Mathematisches Institut, Universität zu Köln, Köln, Germany.
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 304, p. 72-108Article in journal (Refereed) Published
Abstract [en]

In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that discretely preserves the entropy of the system. To guarantee the discrete conservation of entropy requires the addition of a particular source term to the ideal MHD system. Exact entropy conserving schemes cannot dissipate energy at shocks, thus to compute accurate solutions to 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
Academic Press, 2016. Vol. 304, p. 72-108
Keywords [en]
entropy conservation, entropy stable, ideal MHD equations, nonlinear hyperbolic conservation law, finite volume method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156864DOI: 10.1016/j.jcp.2015.09.055ISI: 000365041900004Scopus ID: 2-s2.0-84945298828OAI: oai:DiVA.org:liu-156864DiVA, id: diva2:1315751
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-21Bibliographically approved

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