Time Integration of the Shallow Water Equations in Spherical Geometry

• Published in: Journal of computational physics Vol. 171; no. 1; pp. 373 - 393
• Main Authors: Lanser, D., Blom, J.G., Verwer, J.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 20.07.2001
• Subjects: atmospheric flow; numerical solution of PDEs; SWEs in spherical geometry; Osher's scheme; stereographic coordinates, 65M12, 65M20, 65M06, 86-08, 86A10, 86A17
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.2001.6802

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.