A Method for Incorporating Nested Finite Grids in 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-mesh grid. The interface boundary conditions employed are shown analytically to be the only stable specification of those tested for a simple linear case. Numerical experiments with linear and nonlinear systems in one dimension are used to demonstrate the method by which the fine-mesh region is kept centered over a specified disturbance. Forecast results 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. The evolution of a convective type cell and energy boundary fluxes in the meshed system in shown to compare favorably with the same features in a uniform fine-mesh grid. Future applications of the meshing technique to three-dimensional models is suggested, particularly to problems associated with such disturbances as tropical storms, in which the most significant energy transformations occur in a region of a few grid lengths in most prediction models. Another application may be in ocean circulation models where extra resolution is usually required near the continental boundary regions.