A Stable Finite Difference Scheme for the Linearized Vorticity and Divergence Equation System

Abstract

A modification of Saul'ev's finite difference scheme for the heat equation is applied to the vorticity and divergence equation system for a rotating barotropic fluid. The scheme entails the use of two time levels to approximate second space derivatives, plus alternating ascending and descending marches through the grid lattice. The scheme is unconditionally stable in the von Neumann sense. Test integrations are performed for a linearized problem (the response of a barotropic ocean in a bounded basin to a time varying wind stress) and the truncation error is shown to be low, provided that the time step is short compared to the period of the forcing function.