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A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
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.
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 317, p. 223-256Article in journal (Refereed) Published
Abstract [en]

We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu). The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in FLASH.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 317, p. 223-256
Keywords [en]
magnetohydrodynamics, FLASH, entropy stable, finite volume schemes, pressure positivity
National Category
Computational Mathematics Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:liu:diva-156861DOI: 10.1016/j.jcp.2016.04.048ISI: 000376078600012Scopus ID: 2-s2.0-84964913098OAI: oai:DiVA.org:liu-156861DiVA, id: diva2:1315747
Funder
German Research Foundation (DFG), SPP 1573Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-21Bibliographically approved

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