Global Modelling of the Ocean and Atmosphere Using the Spectral Element Method

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Abstract
The use of spectral methods now has a long history in global atmospheric modelling wherein the attractive properties of Fourier series on spheres, including higher-order convergence rates and efficient implementation via the transform method, have proven advantageous. Partially offsetting these advantages, however, are several competing disadvantages. Two of these, the appearance of Gibbs oscillations for localized processes (e.g., orographic interactions) and the difficulty of mapping spectral techniques onto parallel computer architectures, are inherent to the global nature of these techniques. A third drawback, the restriction of these methods to regular geometries, has severely limited their application to the modelling of the large-scale ocean circulation. We describe a global circulation model that has, in principle, none of these limitations. The model utilizes the spectral element method that combines the geometrical flexibility of traditional finite element methods with the rapid convergence rates of spectral approximation techniques. Simple test problems drawn from both oceanic and atmospheric modelling are used to demonstrate that the resulting model is exponentially convergent, yet allows effective representation of irregular geometry and efficient grid refinement in regions of dynamical interest. Lastly, performance characteristics on the nCUBE/2 and Cray T3D architectures confirm that the element model is ideally suited to the parallel computing environment.