THE CUBED SPHERE - A NEW METHOD FOR THE SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS IN SPHERICAL GEOMETRY

A new gridding technique for the solution of partial differential equa tions in spherical geometry is presented. The method is based on a dec omposition of the sphere into six identical regions, obtained by proje cting the sides of a circumscribed cube onto a spherical surface. By c hoosing the coordinate lines on each region to be arcs of great circle s, one obtains six coordinate systems which are free of any singularit y and define the same metric. Taking full advantage of the symmetry pr operties of the decomposition, a variation of the composite mesh finit e difference method can be applied to couple the six grids and obtain, with a high degree of efficiency, very accurate numerical solutions o f 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 a nd parallel architectures. We present results of two test cases for nu merical approximations to the shallow water equations in spherical geo metry: the linear advection of a cosine bell and the nonlinear evoluti on of a Rossby-Hauriitz wave. Performance analysis for this latter cas e 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. (C) 1996 Academic Pres s, Inc.