A Fast Numerical Method for Explicit Integration of the Primitive Equations near the Poles.

Michael E. Schlesinger

Expert InsightsPublished 1976

As increasingly higher-frequency inertia-gravity waves are resolved, the maximum stable time step decreases toward the poles. Arakawa has developed a three-point method and a Fourier method to modify frequencies of these waves such that, without Fourier filtering or reducing longitudinal resolution, they are stable for a time step based on a prescribed constant length scale. The three-point method is analyzed and compared to the Fourier method. A suitable redefinition of the latitudinally-dependent parameters gives a three point method that is stable with the time step of the Fourier method. Consequently the three-point and Fourier methods are combined to form hybrid method twice as fast as the original Fourier method. The speed of hybrid method is doubled by an improvement of Fourier Transform used in the Fourier method. The hybrid method has increased the time step of the RAND atmospheric GCM from six to ten minutes resulting in decreased time requirement of 37 percent. 50 pp. Ref.

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Schlesinger, Michael E., A Fast Numerical Method for Explicit Integration of the Primitive Equations near the Poles. Santa Monica, CA: RAND Corporation, 1976. https://www.rand.org/pubs/papers/P5507.html.
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