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Time Integration of the Shallow Water Equations in Spherical Geometry

By D. Lanser, J. G. Blom and J. G. Verwer


The shallow water equations in spherical geometry provide a prototype for developing and testing numerical algorithms for atmospheric circulation models. In a previous paper we have studied a spatial discretization of these equations based on an Osher-type finite-volume method on stereographic and latitude-longitude grids. The current paper is a companion devoted to time integration. Our main aim is to discuss and demonstrate a third-order, A-stable, Runge-Kutta-Rosenbrock method. To reduce the costs related to the linear algebra operations, this linearly implicit method is combined with approximate matrix factorization. Its efficiency is demonstrated by comparison with a classical third-order explicit Runge-Kutta method. For that purpose we use a known test set from literature. The comparison shows that the Rosenbrock method is by far superior

Topics: Numerical time integration, spherical shallow water equations. Note, Work carried out under project MAS1.1- Atmospheric Flow and Transport Problems
Year: 2000
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