Finite elements for shallow-water equation ocean models

Monthly Weather Review

Volumn 126, Issue 7, 1998, Pages 1931-1951

  Le Roux, Daniel Y ^a   Staniforth, Andrew ^b   Lin, Charles A ^a  

^a MCGILL UNIVERSITY   (Canada)

^b ENVIRONMENT CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; GRAVITY WAVE; SHALLOW-WATER EQUATION;

EID: 0032427013     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(1998)126<1931:FEFSWE>2.0.CO;2     Document Type: Article

References (52)

1. Arakawa, A., 1966: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I. J. Comput. Phys., 1, 119-143.
2. _, and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA General Circulation Model. Methods Comput. Phys., 17, 173-265.
3. Babuska, I., 1971: Error bounds for finite-element method. Numer. Math., 16, 322-333.
4. Batteen, M. L., and Y. J. Han, 1981: On the computational noise of finite-difference schemes used in ocean models. Tellus, 33, 387-396.
5. Bercovier, M., and O. Pironneau, 1979: Error estimates for the finite element method solution of the Stokes problem in the primitive variables. Numer. Math., 33, 211-224.
6. Brebbia, C. A., and P. W. Partridge, 1976a: Finite element models for circulation studies. Mathematical Models for Environmental Problems, C. A. Brebbia, Ed., Wiley, 141.
7. _, and _, 1976b: Finite element simulation of water circulation in the North Sea. Appl. Math. Model., 1, 101-107.
8. Brezzi, F., 1974: On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. R.A.I.R.O., 8, 129-151.
9. _, and M. Fortin, 1991: Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics, Vol. 15, Springer-Verlag. 350 pp.
10. Crouzeix, M., and P. A. Raviart, 1973: Conforming and non-conforming finite-element methods for solving the stationary Stokes equations. R.A.I.R.O. Anal. Numer., 7, 33-76.
11. Cullen, M. J. P., 1976: On the use of artificial smoothing in Galerkin and finite-difference solutions of the primitive equations. Quart. J. Roy. Meteor. Soc., 102, 77-93.
12. _, and C. D. Hall, 1979: Forecasting and general circulation results from finite-element models. Quart. J. Roy. Meteor. Soc., 105, 571-592.
13. Dutto, L. C., 1993: On the iterative methods for solving linear systems of equations. Eur. J. Finite Elem., 2, 423-448.
14. Engelman, M. S., R. L. Sani, and P. M. Gresho, 1982: The implementation of normal and/or tangential boundary conditions in finite-element codes for incompressible fluid flow. Int. J. Numer. Methods Fluids, 2, 225-238.
15. Foreman, M. G. G., 1984: A two-dimensional dispersion analysis of selected methods for solving the linearized shallow-water equations. J. Comput. Phys., 56, 287-323.
16. Fortin, M., and R. Pierre, 1992: Stability analysis of discrete generalized Stokes problems. Numer. Methods Partial Differential Equations, 8, 303-323.
17. _, H. Manouzi, and A. Soulaimani, 1993: On finite-element approximation and stabilization methods for compressible viscous flows. Int. J. Numer. Methods Fluids, 17, 477-499.
18. Gates, W. L., 1968: A numerical study of transient Rossby waves in a wind-driven homogeneous ocean. J. Atmos. Sci., 25, 3-22.
19. Gill, A. E., 1982: Atmosphere-Ocean Dynamics. International Geophysical Series, Vol. 31, Academic Press, 662 pp.
20. Girault, V., and P. A. Raviart, 1986: Finite Element Methods for Navier-Stokes Equations. Springer Series in Computational Mathematics, Vol. 5, Springer-Verlag, 374 pp.
21. Gray, W. G., 1980: Do finite-element models simulate surface flow? Finite Elements in Water Resources: Proceedings of the Third Int. Conf. on Finite Elements in Water Resources, University, MS, University of Mississippi, 1.122-1.136.
22. _, 1984: On normal flow boundary conditions in finite element codes for two-dimensional shallow-water flow. Int. J. Numer. Methods Fluids, 4, 99-104.
23. _, and D. R. Lynch, 1979: On the control of noise in finite-element tidal computations: A semi-implicit approach. Comput. Fluids, 7, 47-67.
24. Gunzburger, M. D., 1989: Finite Element Methods for Viscous Incompressible Flows: A Guide to the Theory, Practice and Algorithms. Academic Press, 269 pp.
25. Hood, P., and C. Taylor, 1974: Navier-Stokes equations using mixed interpolation. Finite Elements in Flow Problems, J. T. Oden et al., Eds., University of Alabama in Huntsville (UAH) Press, 121-132.
26. Hua, B. L., and F. Thomasset, 1984: A noise-free finite-element scheme for the two-layer shallow-water equations. Tellus, 36A, 157-165.
27. Kelley, R. G., and R. T. Williams, 1976: A finite-element prediction model with variable element sizes. Naval Postgraduate School Rep. NPS-63Wu76101, 109 pp. [Available from Naval Post-graduate School, Monterey, CA 93943.]
28. Kellogg, R. B., and B. Liu, 1996: A finite-element method for the compressible Stokes equations. SIAM J. Numer. Anal., 33, 780-788.
29. Ladyzhenskaya, O. A., 1969: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, 224 pp.
30. LeBlond, P. H., and L. A. Mysak, 1978: Waves in the Ocean. Elsevier, 602 pp.
31. Le Roux, D. Y., C. A. Lin, and A. Staniforth, 1997: An accurate interpolating scheme for semi-Lagrangian advection on an unstructured mesh for ocean modeling. Tellus, 49A, 119-138.
32. Lynch, D. R., and W. G. Gray, 1979: A wave-equation model for finite-element tidal computations. Comput. Fluids, 7, 207-228.
33. Ozell, B., R. Camarero, A. Garon, and F. Guibault, 1995: Analysis and visualization tools in CFD, part I: A configurable data extraction environment. Finite Elem. in Anal. Des., 19, 295-307.
34. 0-approximations for the computation of incompressible flows. Comput. Methods Appl. Mech. Eng., 68, 205-227.
35. Robert, A., 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.-Ocean, 19, 35-46.
36. _, 1982: A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. J. Meteor. Soc. Japan, 60, 319-325.
37. _, J. Henderson, and C. Turnbull, 1972: An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Rev., 100, 329-335.
38. Sani, R. L., P. M. Gresho, R. L. Lee, and D. Griffiths, 1981a: The cause and cure (!) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. Part 1. Int. J. Numer. Methods Fluids, 1, 17-43.
39. _, _, _, and _, 1981b: The cause and cure (!) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. Part 2. Int. J. Numer. Methods Fluids, 1, 171-204.
40. Schoenstadt, A., 1980: A transfer function analysis of numerical schemes used to simulate geostrophic adjustment. Mon. Wea. Rev., 108, 1248-1259.
41. Staniforth, A., and H. L. Mitchell, 1977: A semi-implicit finite-element barotropic model. Mon. Wea. Rev., 105, 154-169.
42. _, and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models: A review. Mon. Wea. Rev., 119, 2206-2223.
43. Temam, R., 1977: Navier-Stokes Equations: Theory and Numerical Analysis. North Holland Publishing Co., 500 pp.
44. Temperton, C., and A. Staniforth, 1987: An efficient two-time level semi-Lagrangian semi-implicit integration scheme. Quart. J. Roy. Meteor. Soc., 113, 1025-1039.
45. Thomasset, F., 1981: Implementation of Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, 159 pp.
46. Walters, R. A., 1983: Numerically induced oscillations in finite-element approximations to the shallow-water equations. Int. J. Numer. Methods Fluids, 3, 591-604.
47. _, and R. T. Cheng, 1980: Accuracy of an estuarine hydrodynamic model using smooth elements. Water Resour. Res., 16, 187-195.
48. _, and G. F. Carey, 1983: Analysis of spurious oscillation modes for the shallow-water and Navier-Stokes equations. Comput. Fluids, 11, 51-68.
49. Williams, R. T. 1981: On the formulation of the finite-element prediction models. Mon. Wea. Rev., 109, 463-466.
50. _, and O. C. Zienkiewicz, 1981: Improved finite-element forms for the shallow-water wave equations. Int. J. Numer. Methods Fluids, 1, 81-97.
51. Winninghoff, F., 1968: On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problem on initialization and objective analysis. Ph.D. thesis, University of California, Los Angeles, 161 pp. [Available from Dept. of Meteorology, UCLA, Los Angeles, CA 90095-1361.]
52. Zeng, Q. C. 1986: Some numerical ocean-atmospheric coupling models. Integrated Global Ocean Monitoring: Proceedings of the First International Symposium, Tallin, U.S.S.R.