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A three-dimensional spectral element model for the solution of the hydrostatic primitive equations. (English) Zbl 1047.76089
Summary: We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual \(h\)-\(p\) paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of the model in the idealized/process-oriented limits.

MSC:
76M22 Spectral methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
Software:
chammp
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