Variational integrators for reduced magnetohydrodynamics

Journal Article · Thu Sep 15 04:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.05.047· OSTI ID:22572349

Kraus, Michael ^[1]; Tassi, Emanuele ^[2]; Grasso, Daniela ^[3]

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1. Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching (Germany)
2. Aix-Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 163 avenue de Luminy, case 907, 13288 cedex 9 Marseille (France)
3. ISC-CNR and Politecnico di Torino, Dipartimento Energia, C.so Duca degli Abruzzi 24, 10129 Torino (Italy)

Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.

• OSTI ID: 22572349
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 321; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASTROPHYSICS
CONSERVATION LAWS
EQUATIONS
HAMILTONIANS
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
PLASMA
VARIATIONAL METHODS