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A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
Mathematisches Institut, Universität zu Köln, Köln, Germany.
I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 332, p. 274-289Article in journal (Refereed) Published
Abstract [en]

We describe a unique averaging procedure to design an entropy stable dissipation operator for the ideal magnetohydrodynamic (MHD) and compressible Euler equations. Often in the derivation of an entropy conservative numerical flux function much care is taken in the design and averaging of the entropy conservative numerical flux. We demonstrate in this work that if the discrete dissipation operator is not carefully chosen as well it can have deleterious effects on the numerical approximation. This is particularly true for very strong shocks or high Mach number flows present, for example, in astrophysical simulations. We present the underlying technique of how to construct a unique averaging technique for the discrete dissipation operator. We also demonstrate numerically the increased robustness of the approximation.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 332, p. 274-289
Keywords [en]
ideal magnetohydrodynamics, compressible Euler, entropy stable, dissipation term, high Mach number
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-156855DOI: 10.1016/j.jcp.2016.12.006ISI: 000393250800014Scopus ID: 2-s2.0-85006512226OAI: oai:DiVA.org:liu-156855DiVA, id: diva2:1315782
Funder
German Research Foundation (DFG), SPP 1573Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-23Bibliographically approved

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