Rueda-Ramírez, Andrés M. ORCID: 0000-0001-6557-9162, Hennemann, Sebastian, Hindenlang, Florian J. ORCID: 0000-0002-0439-249X, Winters, Andrew R. ORCID: 0000-0002-5902-1522 and Gassner, Gregor J. ORCID: 0000-0002-1752-1158 (2021). An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing. Technical Report.


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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. ["A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations". JCP, 2020] 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 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.

Item Type: Preprints, Working Papers or Reports (Technical Report)
CreatorsEmailORCIDORCID Put Code
Rueda-Ramírez, Andrés
Hindenlang, Florian
Winters, Andrew
Gassner, Gregor
URN: urn:nbn:de:hbz:38-535502
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2021-08
Date: 6 October 2021
Language: English
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Center for Data and Simulation Science
Subjects: Natural sciences and mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
Compressible MagnetohydrodynamicsEnglish
Shock CapturingEnglish
Entropy StabilityEnglish
Discontinuous Galerkin Spectral Element MethodsEnglish
Refereed: No


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