Article ID Journal Published Year Pages File Type
520540 Journal of Computational Physics 2008 16 Pages PDF
Abstract

Diagonal preconditioners for implicit-unsteady and steady discretizations of the shallow water equations at low- and high-Rossby and drag-number limits are analyzed. For each case, sub and supercritical flow conditions are also considered. Based on the analysis, a preconditioner is derived for use with a multigrid cycle that performs as well as possible under all conditions. In addition, a streamwise-upwind Petrov–Galerkin discretization of the system is presented that is derived from the preconditioned system. Using this discretization, it is demonstrated that for most conditions, the preconditioner gives rapid convergence that is independent of the grid resolution and the flow parameters. Practical tests including an equatorial Rossby soliton and tide propagation over variable bathymetry are simulated to demonstrate the performance of this approach.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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