A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids

  • Authors:

  • R. Kissmann;J. Pomoell

  • Affiliations:

  • ralf.kissman@uibk.ac.at;jens.pomoell@helsinki.fi

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2012

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Abstract

A new semidiscrete finite volume scheme for systems of hyperbolic conservation laws using the constrained transport method to evolve divergence-free vector fields on orthogonal curvilinear grids is presented. Our results are an extension of a semidiscrete central-upwind scheme for hyperbolic conservation laws to the framework of constrained transport methods. In particular, we show that by employing the mathematical framework used to derive the hyperbolic base scheme, a constrained transport method sharing the desired upwind and nonoscillatory characteristics can be obtained. The derivation of the basic framework is performed independent of the intended spatial order of the scheme, opening the possibility for high-order schemes. Thus, the derivation is also independent of the piecewise polynomial reconstruction from the cell-averages. Furthermore, the geometric factors arising due to the orthogonal curvilinear grid are obtained in a consistent way. The accuracy of the scheme is demonstrated by applying the method to the equations of magnetohydrodynamics.