A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and div B = 0

2020/12/08 by Evan S. Gawlik, Gawlik, Evan S., François Gay–Balmaz +2 · 4 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #65M60 #76M10 #76W05 #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Solar and Space Plasma Dynamics #cs.NA #math.NA #msc:65M60 #msc:76M10 #msc:76W05 #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.2012.04122

arxiv created 2020/12/08 · openalex publication_date 2020/12/08 · arxiv updated 2020/12/09 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28

Abstract

We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint div B = 0 to machine precision, both at the spatially and temporally discrete levels.

Cited by

• Structure-Preserving Transfer of Grad-Shafranov Equilibria to Magnetohydrodynamic Solvers
• MRX: A differentiable 3D MHD equilibrium solver without nested flux surfaces
• Structure-preserving finite element approximations of a hybrid relativistic cold fluid-particle model
• Variational discretizations of viscous and resistive magnetohydrodynamics using structure-preserving finite elements

Related

• Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics
• Stable Finite Element Methods Preserving ∇ ⋅ \boldsymbolB = 0 Exactly for MHD Models
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• Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations