A Survey of Finite-Difference Approximations to the Primitive Equations

The linearized primitive equations for a viscous barotropic fluid in a nonrotating frame are used to investigate the stability properties and the accuracy of several explicit finite difference approximations. Four different schemes are described and their qualities examined. For two schemes the exact numerical solution was derived and compared with the true solution of the differential system. Actual computations are performed and the errors in phase and amplitude evaluated to test the theoretical results.