A FINITE-DIFFERENCE APPROXIMATION OF THE PRIMITIVE EQUATIONS FOR A HEXAGONAL GRID ON A PLANE

Abstract

The hexagonal grid based on a partition of the icosahedron has distinct geometrical qualities for the mapping of a sphere and also presents some indexing difficulties. The applicability of this grid to the primitive equations of fluid dynamics is demonstrated, and a finite-difference approximation of these equations is proposed. The basic variables are the mass fluxes from one hexagonal cell to the next through their common boundary. This scheme conserves the total mass, the total momentum, and the total kinetic energy of the fluid as well as the total squared vorticity of a nondivergent flow. A computational test was performed using a hexagonal grid to describe space periodic waves on a nonrotating plane. The systematic variation of total kinetic and potential energy is less than 10?5 after 1,000 time steps.