Abstract
Large-scale geophysical flows are governed by partial differential equations on the surface of a sphere. In this paper we present a high-resolution finite volume method using gnomonic grid mappings to solve equations relevant to geophysical fluid dynamics. The method is a generalization of the wave propagation algorithm of CLAWPACK for domains which lie on curved manifolds. We show that in this finite volume context it becomes possible to regularize the singularities arising from the gnomonic mapping; and thus, it becomes possible to compute the solution to various hyperbolic conservation laws on the surface of a sphere in a globally conservative and accurate way. With a slight modification, this approach can also be used to solve equations on a circular domain
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LeVeque, R.J., Rossmanith, J.A. (2001). A Wave Propagation Algorithm for the Solution of PDEs on the Surface of a Sphere. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_18
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_18
Publisher Name: Birkhäuser, Basel
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