A Constrained Transport Method for the Shallow Water MHD Equations

James A. Rossmanith ()
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James A. Rossmanith: University of Washington, Department of Applied Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 851-860 from Springer

Abstract: 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.

Keywords: Finite Volume Method; Magnetic Potential; Induction Equation; Magnetohydrodynamic Equation; Full Step (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_80

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DOI: 10.1007/978-3-642-55711-8_80

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