A Multiscale Pressure Splitting of the Shallow-Water Equations: I. Formulation and 1D Tests

Journal of Computational Physics

Volumn 166, Issue 1, 2001, Pages 116-151

  Le Maître, Olivier ^a   Levin, Julia ^b   Iskandarani, Mohamed ^c   Knio, Omar M ^d  

^a UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

^b RUTGERS UNIVERSITY   (United States)

^c UNIVERSITY OF MIAMI   (United States)

^d Johns Hopkins University   (United States)

Author keywords

Aymptotic analysis; Filtering; Ocean circulation; Operator splitting; Spectral elements

Indexed keywords

OCEANOGRAPHY; SURFACE WAVES; WATER WAVES;

AYMPTOTIC ANALYSE; FAST-TIME; FREE SURFACES; OCEAN CIRCULATION; OPERATOR-SPLITTING; SHALLOW WATER EQUATIONS; SPECTRAL ELEMENT; SPLITTINGS; TIME STEP; TIME-SCALES;

EQUATIONS OF MOTION;

EID: 0347078362     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6647     Document Type: Article

References (26)

1. K. Bryan, A numerical method for the study of the circulation of the world ocean, J. Comput. Phys. 4, 347-376 (1969).
2. D. B. Haidvogel, J. L. Wilken, and R. Young, A semi-spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates, J. Comput. Phys. 94, 151-185 (1991).
3. J. K. Dukowicz, R. D. Smith, and R. C. Malone, A reformulation and implementation of the Bryan-Cox-Semtner ocean model on the connection machine, J. Atmospheric Oceanic Technol. 10, 195 (1993).
4. N. Pinardi, A. Rosati, and R. C. Pacanowski, The sea-surface pressure formulation of rigid lid models. Implications for altimetric data assimilation studies, J. Mar. Syst. 6, 110-119 (1995).
5. R. L. Higdon, and R. A. de Szoeke, Barotropic-baroclinic time splitting for ocean circulation modeling, J. Comput. Phys. 135, 30-53 (1997).
6. R. L. Higdon, Implementation of a Barotropic-baroclinic time splitting for isopycnic coordinate ocean modeling, J. Comput. Phys. 148, 579-604 (1999).
7. R. Hallberg, Stable split time stepping schemes for large-scale ocean modeling, J. Comput. Phys. 135, 54-65 (1997).
8. R. L. Higdon and A. F. Bennett, Stability analysis of operator splitting for large-scale ocean modelling, J. Comput. Phys. 123, 311-329 (1996).
9. J. K. Dukowicz and R. D. Smith, Implicit free-surface method for the Bryan-Cox-Semtner ocean model, J. Geophys. Res. C 99, 7991 (1994).
10. Y. Wang and K. Hutter, A semi-implicit semispectral primitive equation model for lake circulation dynamics and its stability performance, J. Comput. Phys. 139, 209-241 (1998).
11. R. Klein, Semi-implicit extension of a Godunov-type scheme based on low-Mach-number asymptotics. I. One-dimensional flow, J. Comput. Phys. 121, 213-237 (1995).
12. M. Iskandarani, D. B. Haidvogel, and J. P. Boyd, A staggered spectral element model with application to the oceanic shallow water equations, Int. J. Numer. Meth. Fluids 20, 393-414 (1995).
13. O. Le Maître, M. Iskandarani, J. Levin, and O. M. Knio, A multiple scales pressure splitting of the shallow-water equations II. Two-dimensional tests, in preparation (2001).
14. A. S. Worlikar, O. M. Knio, and R. Klein, Numerical simulation of a thermoacoustic refrigerator, ESAIM Proc. 1, 363-375 (1996).
15. O. M. Knio, A. S. Worlikar, and H. N. Najm, Mixing and chemical reacting in an idealized swirl chamber, in Twenty-Sixth Symposium (International) on Combustion (The Combustion Institute, 1996), pp. 203-209.
16. A. Majda and J. Sethian, The derivation and numerical solution of equations for zero Mach number combustion, Comb. Sci. Tech. 42, 185-205 (1985).
17. T. S. Schneider, N. Botta, K.-J. Geratz, and R. Klein, Extension of finite volume compressible solvers to multi-dimensional, variable-density zero Mach number flows, J. Comput. Phys., in press.
18. C.-D. Munz, S. Roller, R. Klein, and K.-J. Geratz, The extension of incompressible flow solvers to the weakly compressible regime, Theoret. Comput. Fluid Modeling, submitted for publication.
19. A. T. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comput. Phys. 54, 468-488 (1984).
20. E. M. Ronquist, Ph.D. thesis. (Massachusetts Institute of Technology, Cambridge, 1988).
21. G. E. Karniadakis, Spectral element simulation of turbulent flows in complex geometries, Appl. Numer. Math. 6, 85-105 (1989).
22. H. Ma, A spectral element basin model for the shallow water equations, J. Comput. Phys. 109, 133-149 (1993).
23. M. Taylor, J. Tribbia, and M. Iskandarani, The spectral element method for the shallow water equations on the sphere, J. Comput. Phys. 130, 92-108 (1997).
24. J. Levin, M. Iskandarani, and D. B. Haidvogel, A spectral filtering procedure for eddy-resolving simulations with a spectral element ocean model, J. Comput. Phys. 137, 130-154 (1997).
25. J. P. Boyd, Chebyshev and Fourier Spectral Methods, Lecture Notes in Engineering (Springer-Verlag, New York, 1989).
26. J. Levin, M. Iskandarani, and D. B. Haidvogel, A nonconforming spectral element ocean model, Int. J. Numer. Meth. Fluids 34, 495-525 (2000).