ENSLAVED FINITE-DIFFERENCE APPROXIMATIONS FOR QUASI-GEOSTROPHIC SHALLOW FLOWS

We describe a procedure to improve both the accuracy and computational efficiency of finite difference schemes used to simulate the nonlinea r PDEs that govern barotropic two-dimensional geophysical fluid dynami cs. Our underlying strategy is to reduce the truncation error of a giv en difference scheme in such a way that the time step restrictions are not changed. To accomplish this reduction, we use information from th e governing equations in the case of vanishing time derivatives, Our m ethod is based on a change of variables from fine to coarse grids, whi ch allows us to order the various terms that appear and justify furthe r approximations. These approximations lead to algebraic closures for the new higher-order variables, and finally to a new, enslaved scheme. We demonstrate the utility of the procedure for the shallow water equ ations in both periodic and closed basins. In the latter case we prese nt results that demonstrate the ability of the enslaved scheme to capt ure dynamics on scales smaller than those resolved by the original sch eme.