Ruge, John W.; Li, Yong; McCormick, Steve; Brandt, Achi; Bates, J. R. A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based shallow-water model on the sphere. (English) Zbl 0970.76069 SIAM J. Sci. Comput. 21, No. 6, 2381-2395 (2000). The authors develop new formulation of the shallow-water equations on the sphere based on the semi-Lagrangian advection of potential vorticity. In the two-level method, linear terms are treated semi-implicit, but the approximation of the nonlinear terms is typically done by extrapolation. The authors present a multigrid algorithm for solving the resulting system of three coupled nonlinear equation. The results show that the usual optimal multigrid efficiency is obtained. Reviewer: Qin Mengzhao (Beijing) Cited in 1 Document MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 86A05 Hydrology, hydrography, oceanography 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs Keywords:shallow-water equations on sphere; semi-Lagrangian advection; potential vorticity; two-level method; extrapolation; multigrid algorithm; atmospheric modelling PDFBibTeX XMLCite \textit{J. W. Ruge} et al., SIAM J. Sci. Comput. 21, No. 6, 2381--2395 (2000; Zbl 0970.76069) Full Text: DOI