Modified finite difference schemes for geophysical flows

In previous works we developed a method to improve both the accuracy and computational efficiency of a given finite difference scheme used to simulate a geophysical flow. The resulting modified scheme is at least as accurate as the original, has the same time step, and often uses the same spatial stencil. However, in certain parameter regimes it is higher order. In this paper we apply the method to more realistic settings. Specifically, we apply the method to the Navier–Stokes equations and to a sea breeze model.