On grid generation for numerical models of geophysical fluid dynamics

Abstract

A simple geometric condition that defines the class of classical (stereographic, conic and cylindrical) conformal mappings from a sphere onto a plane is derived. The problem of optimization of computational grid for spherical domains is solved in an entire class of conformal mappings on spherical (geodesic) disk. The characteristics of computational grids of classical mappings are compared for different spherical radii of geodesic disk. For a rectangular computational domain, the optimization problem is solved in the class of classical mappings and respective area of the spherical domain is evaluated.

On Conformal Conic Mappings of Spherical Domains

“…On homogeneous computational grid, the physical mesh size usually varies providing better actual (physical) approximation in the regions where the mapping factor m has the maximum values ( m max ) and worse approximation in the regions with the minimum mapping factor ( m min ). As a measure of the homogeneity of the computational grid one can use the ratio between the maximum and minimum values of the mapping factor over the considered domain: In particular, this criterion is suitable for generation of computational grids for explicit and semi-implicit schemes [ 1 , 7 , 8 ]. As far as we know, the use of the variation coefficient α for measuring the homogeneity of the computational grids was first proposed and studied in [ 1 ] and the further analysis of the properties of this coefficient and justification of its application in the atmosphere-ocean numerical models was performed in different works of the same authors (e.g., [ 4 , 7 , 8 ]).…”