A Constrained Transport Method for the Shallow Water MHD Equations

Abstract

We present in this paper a finite volume method for solving the shallow water magnetohydrodynamic equations. This method uses a constrained transport approach in order to guarantee that the magnetic field satisfies a discrete divergencefree constraint. We briefly review three versions of the constrained transport method that appear in the literature and discuss some of their shortcomings. In order to overcome these difficulties, a new constrained transport method based on advecting the magnetic potential is introduced. Using a common base scheme, these four methods are then applied to a two-dimensional test problem.