Variational Integrators for Ideal Magnetohydrodynamics

Abstract

A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their geometrical character. The resulting numerical method is free of numerical resistivity, thus the magnetic field line topology is preserved and unphysical reconnection is absent. In 2D numerical examples we find that important conservation laws like total energy, magnetic helicity and cross helicity are satisfied within machine accuracy.