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

• Published in: Journal of computational physics Vol. 450; p. 110847
• Main Authors: Gawlik, Evan S., Gay-Balmaz, François
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.02.2022; Elsevier Science Ltd; Elsevier
• Subjects: Computational physics; Density; Energy-preserving; Exactly divergence-free; Finite element; Finite element analysis; Finite element method; Fluid flow; Helicity; Incompressibility; Incompressible flow; Magnetohydrodynamics; Sciences of the Universe; Structure-preserving; Exactly divergence-free; Magnetohydrodynamics; Structure-preserving; Energy-preserving; Helicity; Finite element
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110847

•A finite element method for inhomogeneous, incompressible MHD is presented.•It preserves energy, magnetic helicity, mass, and total squared density.•When the fluid density is constant, the method also preserves cross-helicity.•The method preserves incompressibility and divB=0 pointwise.•These quantities are preserved at both the spatially and temporally discrete levels. 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 divB=0 to machine precision, both at the spatially and temporally discrete levels.