Time integration of the shallow water equations in spherical geometry
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.
|Partial Differential Equations (acm G.1.8)|
|Stability and convergence of numerical methods (msc 65M12), Method of lines (msc 65M20), Finite difference methods (msc 65M06)|
|Modelling, Analysis and Simulation [MAS]|
Lanser, D, Blom, J.G, & Verwer, J.G. (2000). Time integration of the shallow water equations in spherical geometry. Modelling, Analysis and Simulation [MAS]. CWI.