A method for incorporating nested finite grids into the solution of systems of geophysical equations.

Abstract

A numerical technique with simultaneous time integration of a meshed grid system is proposed, in which the fine mesh region is able to move within the coarse grid. The interface boundary conditions employed are shown analytically to be the only stable specification of those tested for a simple linear case. Numerical solutions using the meshed system are compared with those from uniform coarse and fine grids. One important criterion is that the solution within the fine mesh region of the meshed grid must have nearly the same accuracy as in a system which uses a fine mesh everywhere. The technique is applied to a two-dimensional (y,p) ten-level primitive equation model. Behavior of the meshed model is examined in experiments in which a small scale heat source is imbedded within an undisturbed zonal flow pattern. Energy boundary fluxes across the interface in the meshed system are shown to compare favorably with those in a uniform fine mesh grid. Three-dimensional (x,y,p) versions of the primitive equation model with single and multiple grid reductions are also examined. Simulated small scale disturbances are used to compare the meshed model solutions with those obtained on a uniform grid. Future applications of the meshing technique are suggested, such as in tropical storm research and general circulation models of the atmosphere and ocean.