Nonlinear shallow‐water equations on the Yin‐Yang grid

Abstract

AbstractThe system of nonlinear shallow‐water equations (SWEs) is a hyperbolic system serving as a primary test problem for numerical methods used in modelling global atmospheric flows. In this article, the SWEs on a rotating sphere are solved on the Yin‐Yang grid by using a domain decomposition method (DDM). This overset grid is singularity free and has a quasi‐uniform grid spacing. It is composed of two identical latitude/longitude orthogonal grid panels that are combined to cover the sphere with partial overlap on their boundaries. On each of the two subgrids, the local solver is based on an implicit and semi‐Lagrangian discretization on a horizontally staggered Arakawa C mesh. The resulting positive definite Helmholtz problem is solved using a Schwarz‐type DDM known as the optimized Schwarz method, which gives better performance than the classical Schwarz method by using specific Robin or higher‐order transmission conditions. Finally, the standard shallow‐water test set is performed in order to show that the DDM solution for SWEs on the Yin‐Yang grid system can reproduce the global solution accurately on the sphere. This work represents a first step in the development of a three‐dimensional forecasting model on the Yin‐Yang grid. © 2011 Crown in the right of Canada. Published by John Wiley & Sons Ltd.