A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell

Abstract

A numerical solution technique for the axisymmetric flow in a differentially heated, rotating spherical annulus is developed. This method, based on the incompressible Navier-Stokes equations, simulates the Atmospheric General Circulation Experiment (AGCE) proposed for a future Shuttle mission. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This pseudospectral/finite difference (PS/FD) method is applied to a hierarchy of cases of varying difficulty. The difficult cases are characterized by thinner Ekman layers resulting from higher rotation rates, larger difference in boundary temperatures, and stronger body forces. Comparison of the results establishes the higher accuracy and efficiency of the PS/FD method over the pure second-order accurate finite difference (FD) method. This paper discusses the development and performance of a mixed PS/FD model for the AGCE which has been modelled in the past only by pure FD formulations.