An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes (Communications in Computational Physics, 2018)
In this paper we consider a discontinuous Galerkin discretization of theideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergencefree constraint (∇·B = 0) of its magnetic field B. We first present two approachesfor maintaining the divergence free constraint, namely the approach of a locallydivergence free projection inspired by locally divergence free elements [19], andanother approach of the divergence cleaning technique given by Dedner et al. [15]. Bycombining these two approaches we obtain an efficient method at the almost same numericalcost. Finally, numerical experiments are performed to show the capacity andefficiency of the scheme.