Staggered Turkel-Zwas Schemes for Two-Dimensional Shallow-Water Equations

Abstract

The Turkel-Zwas-type schemes employ coarse grids to discretize the terms associated with the fast gravity-inertia waves and use fine grids to treat the terms associated with the slow Rossby waves. The ratio of the coarse and fine grids is an integer, p>1, and one can use time steps nearly p times larger than those allowed by the Courant-Friedrich-Lewy condition for the usual explicit leapfrog scheme. This paper investigates the Turkel-Zwas-type schemes with three spatial grids-namely, A (unstaggered), B, and C grids (staggered)-for two-dimensional shallow-water equations. A new method that uses the Laplace transform is introduced to solve the two-dimensional phase solutions. Comparisons of the three grids with coarse and fine-grid resolutions are made. One realistic model problem is tested to verify the linear analysis results. The test shows that the Turkel-Zwas-type schemes can be used for a larger time step in some practical simulations.