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A structure-preserving finite element method for compressible ideal and resistive magnetohydrodynamics

Part of: Hamiltonian Methods in Plasma Physics

Published online by Cambridge University Press:  17 September 2021

Evan S. Gawlik Open the ORCID record for Evan S. Gawlik [Opens in a new window]  and
François Gay-Balmaz Open the ORCID record for François Gay-Balmaz [Opens in a new window]
Evan S. Gawlik
Affiliation:
Department of Mathematics, University of Hawai‘i at Mānoa
François Gay-Balmaz*
Affiliation:
CNRS - LMD, Ecole Normale Supérieure, Paris
*
†Email address for correspondence: francois.gay-balmaz@lmd.ens.fr
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Abstract

We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from the geometric variational formulation of the equations. It preserves the balance laws governing the evolution of total energy and magnetic helicity, and preserves mass and the constraint $\text {div}B = 0$ to machine precision, both at the spatially and temporally discrete levels. In particular, conservation of energy and magnetic helicity hold at the discrete levels in the ideal case. It is observed that cross-helicity is well conserved in our simulation in the ideal case.

Keywords

plasma simulationplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 5 , October 2021 , 835870501
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

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