zbMATH — the first resource for mathematics

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.

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
Full Text: DOI
[1] Boyd, J.P., Chebyshev and Fourier spectral methods, Lecture notes in engineering, (1989), Springer New York
[2] Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, Springer series in computational physics, (1988), Springer New York
[3] Cockburn, B., An introduction to the discontinuous Galerkin method for convection dominated flows, (), 151-268 · Zbl 0927.65120
[4] Curchitser, E.N.; Haidvogel, D.B.; Iskandarani, M., On the transient adjustment of a mid-latitude abyssal Ocean basin with realistic geometry: the constant depth limit, Dynamics of atmosphere and oceans, 29, 2-4, 147, (1999)
[5] Curchitser, E.N.; Haidvogel, D.B.; Iskandarani, M., On the transient adjustment of a mid-latitude abyssal Ocean basin with realistic geometry and bathymetry, Journal of physical oceanography, 31, 3, 725, (2001)
[6] Curchitser, E.N.; Iskandarani, M.; Haidvogel, D.B., A spectral element solution of the shallow water equations on multiprocessor computers, Journal of atmospheric and oceanographic technology, 15, 2, 510-521, (1998)
[7] Haidvogel, D.B.; Beckmann, A., Numerical Ocean circulation modeling, (1999), Imperial College Press · Zbl 0932.76001
[8] Haidvogel, D.B.; Curchitser, E.; Iskandarani, M.; Hughes, R.; Taylor, M.A., Global modeling of the Ocean and atmosphere using the spectral element method, Atmosphere-Ocean, 35, 505-531, (1997)
[9] Higdon, R.L.; Bennett, A.F., Stability analysis of operator splitting for large-scale Ocean modeling, Journal of computational physics, 123, 2, 311, (1996) · Zbl 0863.76045
[10] Iskandarani, M.; Haidvogel, D.B.; Boyd, J.P., A staggered spectral element model with application to the oceanic shallow water equations, International journal for numerical methods in fluids, 20, 393-414, (1995) · Zbl 0870.76057
[11] Karniadakis, G.E.M.; Sherwin, S.J., Spectral/hp element methods for CFD, (1999), Oxford University Press Oxford · Zbl 0954.76001
[12] Large, W.G.; McWilliams, J.C.; Doney, S.C., Oceanic vertical mixing: a review and a model with a non-local boundary layer parameterization, Reviews in geophysics, 32, 363-403, (1994)
[13] Levin, J.; Iskandarani, M.; Haidvogel, D.B., A spectral filtering procedure for eddy-resolving simulations with a spectral element Ocean model, Journal of computational physics, 137, 1, 130-154, (1997) · Zbl 0898.76082
[14] Levin, J.; Iskandarani, M.; Haidvogel, D.B., A nonconforming spectral element Ocean model, International journal for numerical methods in fluids, 34, 6, 495-525, (2000) · Zbl 0997.76065
[15] Lomtev, I.; Kirby, R.M.; Karniadakis, G.E., A discontinuous Galerkin ale method for compressible viscous flows in moving domains, Journal of computational physics, 155, 1, 18-159, (1999) · Zbl 0956.76046
[16] Ma, H., A spectral element basin model for the shallow water equations, Journal of computational physics, 109, 133-149, (1993) · Zbl 0790.76065
[17] Perenne, N.; Haidvogel, D.B.; Boyer, D.L., Laboratory – numerical model comparisons of flow over a coastal canyon, Journal of atmospheric and oceanographic technology, 18, 235-255, (2001)
[18] Song, Y.H., A general pressure gradient formulation for Ocean models. part *1*: scheme design and diagnostic analysis, Monthly weather review, 126, 1, 3213-3230, (1998)
[19] Song, Y.H.; Haidvogel, D.B., A semi-implicit Ocean circulation model using a generalized topography-following coordinate system, Journal of computational physics, 105, 1, 228, (1994) · Zbl 0853.76014
[20] M.A. Taylor, R. Loft, J. Tribbia, Performance of a spectral element atmospheric model (seam) on the hp exemplar spp2000, Technical Report NCAR/TN-439+EDD, National Center for Atmospheric Research, Boulder, CO, 1998
[21] Taylor, M.A.; Tribbia, J.; Iskandarani, M., The spectral element method for the shallow water equations on the sphere, Journal of computational physics, 130, 1, 92-108, (1997) · Zbl 0868.76072
[22] Taylor, M.A.; Wingate, B.A., A generalized diagonal mass matrix spectral element method for non-quadrilateral elements, Applied numerical mathematics, 33, 1/4, 259, (2000) · Zbl 0964.65107
[23] Taylor, M.A.; Wingate, B.A.; Vincent, R.E., An algorithm for computing Fekete points in the triangle, SIAM journal on numerical analysis, 33, 5, 1707-1720, (2000) · Zbl 0986.65017
[24] Wang, D.-P., Mutual intrusion of a gravity current and density front formation, Journal of physical oceanography, 14, 1191-1199, (1984)
[25] Williamson, D.L.; Drake, J.B.; Hack, J.J.; Jakob, R.; Swarztrauber, P.N., A standard test set for the numerical approximations to the shallow water equations in spherical geometry, Journal of computational physics, 102, 211-224, (1992) · Zbl 0756.76060
[26] B.A. Wingate, J.P. Boyd, Spectral element methods on triangles for geophysical fluid dynamics problems, In: Proceedings of the Third International Conference On Spectral and High-order Methods, Houston, Texas, 1996, pp. 305-314, Houston Journal of Mathematics
[27] Wunsch, C.; Haidvogel, D.B.; Iskandarani, M.; Hughes, R., Dynamics of the long-period tides, Progress in oceanography, 40, 1/4, 80-108, (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.