An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing

JOURNAL OF COMPUTATIONAL PHYSICS

卷:444

Article

Rueda-Ramirez, Andres M.¹  Hennemann, Sebastian²  Hindenlang, Florian J.³  Winters, Andrew R.⁴  Gassner, Gregor J.¹ 

[1] Univ Cologne, Dept Math & Comp Sci, Weyertal 86-90, D-50931 Cologne, Germany

[2] German Aerosp Ctr DLR, D-51147 Cologne, Germany

[3] Max Planck Inst Plasma Phys, Boltzmannstr 2, D-85748 Garching, Germany

[4] Linkoping Univ, Dept Math, Appl Math, S-58183 Linkoeping, Sweden

关键词: Compressible magnetohydrodynamics;    Shock capturing;    Entropy stability;    Discontinuous Galerkin spectral element methods;   

DOI  :  10.1016/j.jcp.2021.110580

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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