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

Abstract

We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics (MHD) 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 $\mathrm{div}B=0$ 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.

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References in corpus (5)

• Geometric, Variational Discretization of Continuum Theories
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• A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
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Cited by in corpus (3)

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• Extended shallow-water theories with thermodynamics and geometry