We describe a procedure to improve both the accuracy and computational efficiency of finite difference schemes used to simulate the nonlinear PDEs governing barotropic (2D) geophysical fluid dynamics. The underlying goal is to reduce the truncation error of a given difference scheme in such a way that the time step restrictions are not changed. To accomplish this reduction, we use information from the governing equations in the case of vanishing time derivatives. We present an efficient algorithm based on a change of variables from fine to coarse grids which results in a new, `enslaved' scheme. The utility of the procedure is demonstrated for the Shallow Water equations in both periodic and closed basins. In the latter case we present results which demonstrate the ability of the enslaved scheme to capture dynamics on scales smaller than the grid resolution.

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