A central conservative scheme for general rectangular grids

Authors:
R. Kissmann;J. Pomoell;W. Kley
Affiliations:
Institut für Astronomie and Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany;Department of Physics, Gustaf Hällströmin katu 2a, 00014 University of Helsinki, Finland;Institut für Astronomie and Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

We present an extension of the genuinely multi-dimensional semi-discrete central scheme developed in [A. Kurganov, S. Noelle, G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (3) (2001) 707-740.] to arbitrary orthogonal grids. The presented algorithm is constructed to yield the geometric scaling factors in a self-consistent way. Additionally, the order of the scheme is not fixed during the derivation of the basic algorithm. Based on the resulting general scheme it is possible to construct methods of any desired order, just by considering the corresponding reconstruction polynomial. We demonstrate how a second order scheme in plane polar coordinates and cylindrical coordinates can be derived from our general formulation. Finally, we demonstrate the correctness of this second order scheme through application to several numerical experiments.