Hyperbolic GLM Scheme for Elliptic Constraints in Computational Electromagnetics and MHD

Abstract

The charge conservation laws in general are not strictly obeyed in computational electromagnetics and Magnetohydrodynamics (MHD), due to the presence of various types of numerical errors. In this paper, a field theoretical method for the treatment of the often violated charge conservation laws in computational electrodynamics and MHD has been investigated, which reduces to the well-known hyperbolic Generalized Lagrange Multplier (GLM) scheme under particular constraints. The central idea of our divergence correction scheme is the implementation of the physically consistent counter terms to Maxwell and MHD equations, for the restoration of the charge conservation laws. The underlying idea has been verified by numerical experiments for Maxwell-Vlasov and shallow water MHD systems.