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A standard test set for numerical approximations to the shallow water equations in spherical geometry. (English) Zbl 0756.76060

The numerical methods devised by the authors for solving shallow water equations in spherical geometry are applied to seven test cases presented in order of complexity. The aim, of course, is to perfect a numerical method for climate modelling. The seven cases are as follows: (i) advection of cosine bell over the pole, (ii) steady nonlinear zonal geostrophic flow, (iii) nonlinear steady zonal geostrophic flow with compact support, (iv) forced nonlinear system with a translating low pressure centre, (v) zonal flow over an isolated mountain, (vi) Rossby- Haurwitz wave, and (vii) observed atmospheric states.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76U05 General theory of rotating fluids
76B65 Rossby waves (MSC2010)
86A10 Meteorology and atmospheric physics

Software:

chammp
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References:

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