Journal of the Meteorological Society of Japan. Ser. II
A Semi-Lagrangian and Semi-Implicit Numerical Integration Scheme for the Primitive Meteorological Equations
André Robert
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Volume 60 (1982) Issue 1 Pages 319-325

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A semi-Lagrangian algorithm is associated with the semi-implicit method in the integration of the shallow water equations on a rotating sphere. The resulting model is unconditionally stable and can be integrated with rather large time steps. Truncation errors remain reasonably small with time steps 25 times as large as those used with explicit integration schemes.
An analysis of the proposed method is performed and it indicates that the scheme is stable. Also, the results of a few integrations are presented and from these we conclude that the model is not very sensitive to the size of the time step provided that it does not exceed a value of the order of two or three hours.

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