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A global semi-Lagrangian spectral model for the reformulated shallow water equations

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  • In this paper, we study the semi-Lagrangian spectral method for the shallow-water equations in a rotating, spherical geometry. With the reformulation of a vector calculus identity for spherical geometries, we are able to write the vorticity and divergence equations in advective form and directly apply the semi-Lagrangian, spectral method. The scalar vorticity and divergence equations are used to avoid the pole problems. Shape preserving interpolation is used for the calculation of departure point values for all fields. The results of the standard test set are presented showing accuracy, stability and regularity properties of the method for atmospheric flows.
    Mathematics Subject Classification: Primary: 35Q35, 65Q99, 76M22, 86A10.


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