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 equations in spherical geometry is presented. The method is based on a decomposition of 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. 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. We present results of two test cases for the shallow water equations in spherical geometry: the linear advection of a cosine bell, and the nonlinear evolution of a Rossby-Haurwitz wave.
decomposition of sphere into six identical regions
scientific article; zbMATH DE number 881875