A new gridding technique for the solution of partial differential equations in spherical geometry is presented. The method 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. By choosing the coordinate lines on each region to be arcs of great circles, one obtains six coordinate systems which are free of any singularity and define the same metric. Taking full advantage of the symmetry properties of the decomposition, a variation of the composite mesh finite difference method can be applied to couple the six grids and obtain, with a high degree of efficiency, very accurate numerical solutions of partial differential equations on the sphere. The advantages of this new technique over both spectral and uniform longitude-latitude grid point methods are discussed in the context of applications on serial and parallel architectures. We present results of two test cases for numerical approximations to the shallow water equations in spherical geometry: the linear advection of a cosine bell and the nonlinear evolution of a Rossby-Haurwitz wave. Performance analysis for this latter case indicates that the new method can provide, with substantial savings in execution times, numerical solutions which are as accurate as those obtainable with the spectral transform method. © 1996 Academic Press, Inc.

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