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This project revolves around the development of a new ocean model based on the spectral element method (Patera 1984). The aim is to use the method's attractive properties to improve our ocean simulation capabilities. The spectral element method can be most concisely described as an h-p type Galerkin finite element method which approximates the solution within each element with a high order polynomial. It offers several desirable properties for ocean simulations: geometrical flexibility with a spatial discretization based on unstructured grids, high-order convergence rates, and dense computations at the elemental level leading to extremely good scalability characteristics on parallel computers (Fischer 1989).
Unstructured grid allow better geometrical description of ocean basins,
and permit the use of variable resolution grids tailored to resolve the
dynamical length scales of the circulation (e.g. western boundary
currents like the Gulf Stream). Multi-scale simulations within a single
frame-work are thus possible. This Figure
shows a sample spectral element grid encompassing the whole ocean, and
emphasizing the North Pacific basin; the color code shows the average
grid spacing (km) within each element. The spectral element method is
highly tunable in that it offers a dual approach to convergence:
algebraic and exponential. In addition, its computational efficiency
helps resolve small-scale features like ocean eddies without an
excessive or prohibitive number of degrees of freedom. This last
feature, combined with the scalability of the method, will permit
routine multi-decadal simulations of the oceanic circulation on the
current generation of parallel computers.
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A two-dimensional version of the spectral element ocean model (SEOM) has already been developed and tested thoroughly. It solves the depth-integrated form of the 3D equations: the shallow water equations. The model is described in Iskandarani et al. 1995, and sample applications can be found in several publications. The applications list includes: an investigation of the wind-driven circulation in the Pacific Ocean; a process study of the abyssal circulation in the Eastern Mediterranean; a validation of the atmospheric version of the model on a standard suite of 2D atmospheric tests problems on the sphere; and an investigation of the dynamics of the long period tides in the global ocean.
The validation of the atmospheric version of the spectral element ocean model on the spherical test suite includes comparison to analytical and model results. The tests confirm that spectral elements have most of the advantages of spherical harmonics including exponential converge under p-refinement, and the avoidance of polar singularities. In addition, spectral elements allow for local refinement of the mesh, high-order algebraic convergence under h-refinement, and complete parallelism.
A parallel version of the 2D code was developed and tested for scalability. It relies on a domain-decomposition approach to divide the work among processors, and on explicit message passing for communication. The code was originally implemented in the C-language on the nCUBE-2 hypercube using its native communication software. We have since recoded all our models (2D, multi-layer and 3D) in F90, and changed the communication library to MPI. The parallel code is highly portable and we have been able to run it on Cray T3D and T3E, IBM SP2, HP-Exemplar, SGI O2K, and our own home-brewed, Bewolf-type, Ultra-SPARC parallel computing cluster. For more information on the parallelism of SEOM, please refer to the parallel link on the navigation window.