A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Evan S. Gawlik , François Gay-Balmaz (1)

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)

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.

Keywords: Magnetohydrodynamics; Structure-preserving; Energy-preserving; Exactly divergence-free; Helicity; Finite element

Domains: Sciences of the Universe [physics]

Evan S. Gawlik, François Gay-Balmaz. A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0. Journal of Computational Physics, 2022, 450, ⟨10.1016/j.jcp.2021.110847⟩. ⟨insu-03726924⟩