Finite difference approximation to the shallow water equations on a quasi-uniform spherical grid

Abstract

A new gridding technique for the solution of partial differential equations in spherical geometry is applied to the shallow water equations. The method, named the ‘Cubed-Sphere’, is based on a decomposition of the sphere into six identical regions, obtained by projecting the sides of a circumscribed cube onto a spherical surface. The grids defined on each of the six regions are coupled through an interopolation procedure based on the composite mesh finite difference method. We present results from two test cases: the integration of a steady state zonal geostrophic flow and the evolution of a Rossby-Haurwitz wave. For this latter case, the performance of the ‘Cubed-Sphere’ method will also be compared in terms of accuracy and execution time to those obtained using the spectral transform method. Finally, for the Rossby-Haurwitz test case we also give performance and scalability results obtained with a parallel version of the ‘Cubed-Sphere’ method run on a 25 Gflops (512 nodes) APE100/Quadrics massively parallel computer.