Finite Difference Approximation to the Shallow Water Equations on a Quasi-Uniform Spherical Grid

摘要

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 interopola-tion 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.