Abstract
The Super Compact Finite Difference Method (SCFDM) is applied to spatial differencing of some prototype linear and nonlinear geophysical fluid dynamics problems. For the frequency of linear inertia-gravity waves on different numerical grids (Arakawa’s A-E and Randall’s Z), the sixth-order SCFDM shows a substantial improvement on the conventional methods. For the Jacobians involved in vorticity advection by nondivergent flow and in Bolin-Charney balance equation, as nonlinear problems, it is found that the sixth-order SCFDM provides a noticeably more accurate representation of the wavenumber distribution of the Jacobians, when compared with the conventional methods. In addition, computation of a normalized global error at different horizontal resolutions in longitude and latitude directions for the Rossby-Haurwitz wave on a sphere shows that sixth-order SCFDM can markedly improve on the fourth-order compact.
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