Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates

B. Neta, F.X. Giraldo, I.M. Navon

A linear analysis of the shallow water equations in spherical coordinates for the Turkel-Zwas (T-Z)[1] explicit large time-step scheme is presented. This paper complements the results of Schoenstadt,[2] Neta and Navon[3] and others in 1-D, and of Neta and DeVito[4] in 2-D, but applied to the spherical coordinate case of the T-Z scheme. This coordinate system is more realistic in meteorology and more complicated to analyze, since the coefficients are no longer constant.The analysis suggests that the t-Z scheme must be staggered in a certain way to get the eigenvalues and eigenfunctions approaching those of the continuous case.The importance of such an analysis is the fact that it is also valid for nonconstant coefficients and thereby applicable to any numerical scheme.Numerical experiments comparing the original (unstaggered) and staggered versions of the T-Z scheme are presented.These experiments corroborate the analysis showing the improvements gained by staggering the Turkel-Zwas scheme.