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Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
Mathematisches Institut, Universität zu Köln, Köln, Germany.ORCID iD: 0000-0002-5902-1522
Mathematisches Institut, Universität zu Köln, Köln, Germany.
I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
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2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 420-467Article in journal (Refereed) Published
Abstract [en]

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme).

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 364, p. 420-467
Keywords [en]
magnetohydrodynamics, entropy stability, divergence-free magnetic field, divergence cleaning
National Category
Computational Mathematics Other Physics Topics
Identifiers
URN: urn:nbn:se:liu:diva-156853DOI: 10.1016/j.jcp.2018.03.002ISI: 000432481000020Scopus ID: 2-s2.0-85045397430OAI: oai:DiVA.org:liu-156853DiVA, id: diva2:1315777
Funder
EU, European Research Council, 679852EU, European Research Council, 714487German Research Foundation (DFG), SPP 1573Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-23Bibliographically approved

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The full text will be freely available from 2020-07-13 08:00
Available from 2020-07-13 08:00

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Winters, Andrew Ross

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