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A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based shallow-water model on the sphere. (English) Zbl 0970.76069

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.

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
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