Comparison of different spatial grids for numerical schemes of geophysical fluid dynamics (Q1012511)

Conformal mappings are used in geophysical fluid dynamics to the problem of flattening the Earth's surface. The most uniform grids of spherical domains are discussed. Stereographic, cylindrical and conic grids for computational rectangles are developed and their uniformity is compared. Numerical experiments for the nonlinear shallow water equations are performed in order to assess the practical efficiency of the constructed grids and to compare the numerical results with analytical evaluations.