Universität zu Köln

Rueda-Ramirez, Andres M., Hennemann, Sebastian, Hindenlang, Florian J., Winters, Andrew R. and Gassner, Gregor J. (2021). An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. J. Comput. Phys., 444. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2716

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Abstract

The second paper of this series presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible magneto-hydrodynamics (MHD) equations. Specifically, we use the resistive GLM-MHD equations, which include a divergence cleaning mechanism that is based on a generalized Lagrange multiplier (GLM). For the continuous entropy analysis to hold, and due to the divergence-free constraint on the magnetic field, the GLM-MHD system requires the use of non-conservative terms, which need special treatment. Hennemann et al. (2020) [25] recently presented an entropy stable shock-capturing strategy for DGSEM discretizations of the Euler equations that blends the DGSEM scheme with a subcell first-order finite volume (FV) method. Our first contribution is the extension of the method of Hennemann et al. to systems with non-conservative terms, such as the GLM-MHD equations. In our approach, the advective and non-conservative terms of the equations are discretized with a hybrid FV/DGSEM scheme, whereas the visco-resistive terms are discretized only with the high-order DGSEM method. We prove that the extended method is semi-discretely entropy stable on three-dimensional unstructured curvilinear meshes. Our second contribution is the derivation and analysis of a second entropy stable shock-capturing method that provides enhanced resolution by using a subcell reconstruction procedure that is carefully built to ensure entropy stability. We provide a numerical verification of the properties of the hybrid FV/DGSEM schemes on curvilinear meshes and show their robustness and accuracy with common benchmark cases, such as the Orszag-Tang vortex and the GEM (Geospace Environmental Modeling) reconnection challenge. Finally, we simulate a space physics application: the interaction of Jupiter's magnetic field with the plasma torus generated by the moon Io. (C) 2021 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rueda-Ramirez, Andres M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hennemann, Sebastian UNSPECIFIED UNSPECIFIED UNSPECIFIED Hindenlang, Florian J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-588126
DOI:	10.1016/j.jcp.2021.110580
Journal or Publication Title:	J. Comput. Phys.
Volume:	444
Date:	2021
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2716
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NONLINEAR CONSERVATION-LAWS; IDEAL COMPRESSIBLE MHD; ELEMENT-METHOD; SCHEMES; SYSTEMS; EULER; MAGNETOHYDRODYNAMICS; DISCRETIZATION Multiple languages Computer Science, Interdisciplinary Applications; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58812