A parallel well-balanced finite volume method for shallow water equations with topography on the cubed-sphere

Authors:
Chao Yang;Xiao-Chuan Cai
Affiliations:
Institute of Software, Chinese Academy of Sciences, Beijing 100190, PR China;Department of Computer Science, University of Colorado at Boulder, Boulder, CO 80309, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

A finite volume scheme for the global shallow water model on the cubed-sphere mesh is proposed and studied in this paper. The new cell-centered scheme is based on Osher's Riemann solver together with a high-order spatial reconstruction. On each patch interface of the cubed-sphere only one layer of ghost cells is needed in the scheme and the numerical flux is calculated symmetrically across the interface to ensure the numerical conservation of total mass. The discretization of the topographic term in the equation is properly modified in a well-balanced manner to suppress spurious oscillations when the bottom topography is non-smooth. Numerical results for several test cases including a steady-state nonlinear geostrophic flow and a zonal flow over an isolated mountain are provided to show the flexibility of the scheme. Some parallel implementation details as well as some performance results on a parallel supercomputer with more than one thousand processor cores are also provided.