A staggered spectral element model with application to the oceanic shallow water equations

Abstract

Abstract A staggered spectral element model for the solution of the oceanic shallow water equations is presented. We introduce and compare both an implicit and an explicit time integration scheme. The former splits the equations with the operator‐integration factor method and solves the resulting algebraic system with generalized minimum residual (GMRES) iterations. Comparison of the two schemes shows the performance of the implicit scheme to lag that of the explicit scheme because of the unpreconditioned implementation of GMRES. The explicit code is successfully applied to various geophysical flows in idealized and realistic basins, notably to the wind‐driven circulation in the North Atlantic Ocean. The last experiment reveals the geometric versatility of the spectral element method and the effectiveness of the staggering in eliminating sprious pressure modes when the flow is nearly non‐divergent.