Vertical discretization in tidal flow simulations

International Journal for Numerical Methods in Fluids

Volumn 22, Issue 9, 1996, Pages 815-834

  Fortunato, André B ^a   Baptista, António M ^a  

^a OREGON HEALTH AND SCIENCE UNIVERSITY   (United States)

Author keywords

Localized sigma co ordinates; Numerical experimentation; Sigma co ordinates; Tidal flow; Vertical discretization

Indexed keywords

COMPUTER SIMULATION; ERRORS; ESTUARIES; NUMERICAL METHODS; TIDES;

LOCALIZED SIGMA COORDINATES; TIDAL FLOW; VERTICAL DISCRETIZATION;

FLOW OF FLUIDS;

EMPIRICAL LAW; TIDAL MODELS; VERTICAL DISCRETIZATION;

EID: 0029667069     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19960515)22:9<811::aid-fld375>3.0.co;2-h     Document Type: Article

References (33)

1. J. J. Leendertse and S. K. Liu, 'A three-dimensional model for estuaries and coastal seas. II. Aspects of computation', Rand Corporation Rep. R-1764-OWRT, 1975.
2. V. Casulli and R. T. Cheng, 'Semi-implicit finite difference methods for three-dimensional shallow water flow', Int. j. numer. methods fluids, 15, 629-648 (1992).
3. A. F. Blumberg and G. L. Mellor, 'A description of a three- dimensional coastal ocean circulation model', in N. S. Heaps (ed.), Three-Dimensional Coastal Ocean Models, CES Vol. 4, AGU, Washington, DC, 1987, pp. 1-16.
4. D. R. Lynch and F. E. Werner, 'Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model', Int. j. numer. methods fluids, 12, 507-533 (1991).
5. R. A. Walters, 'A 3D, finite element model for coastal and estuarine circulation', Continental Shelf Res., 12, 83-102 (1992).
6. R. T. Cheng and P. E. Smith, 'A survey of three-dimensional numerical estuarine models', Proc. Conf. on Estuarine and Coastal Modeling, ASCE, New York, 1990, pp. 1-15.
7. J. M. Gary, 'Estimate of truncation error in transformed coordinate, primitive equation atmospheric models', J. Atmos. Sci., 30, 223-233 (1973).
8. R. L. Haney, 'On the pressure gradient force over steep topography in sigma coordinate ocean models', J. Phys. Oceanogr., 21, 610-619 (1991).
9. E. Deleersnijder and J. M. Beckers, 'On the use of the σ- coordinate system in regions of large bathymetric variation', J. Marine Syst., 3, 381-390 (1992).
10. R. P. Signell, H. L. Jenter and A. F. Blumberg, 'Modeling the Seasonal Circulation in Massachussets Bay', Proc. 3rd Int. Conf. on Estuarine and Coastal Modeling, ASCE, New York, 1994, pp. 578-590.
11. J. D. McCalpin, 'A comparison of second-order and fourth-order pressure gradient algorithms in a σ-coordinate ocean model', Int. j. numer. methods fluids, 18, 361-383 (1994).
12. G. S. Stelling and J. A. Th. M. van Kester, 'On the approximation of horizontal gradients in sigma coordinates for bathymetry with steep bottom slopes', Int. j. numer. methods fluids, 18, 915-935 (1994).
13. A. B. Fortunato and A. M. Baptista, 'Modeling near-bottom advective acceleration in surface water models', Proc. Int. Conf. on Computational Methods in Water Resources X, Kluwer, Dordrecht, 1994, pp. 1045-1052.
14. A. B. Fortunato and A. M. Baptista, 'Localized sigma coordinates for the vertical structure of hydrodynamic models', Proc. 3rd Int. Conf. on Estuarine and Coastal Modeling, ASCE, New York, 1994, pp. 323-335.
15. J. P. Laible, 'On the solution of the three-dimensional shallow water equations using the wave equation formulation', Proc. Int. Conf. on Computational Methods in Water Resources IX, Computational Mechanics Publications, Southampton, 1992, pp. 545-552.
16. A. B. Fortunato and A. M. Baptista, 'A comparison of two methods to evaluate horizontal gradients in surface water models', Atmos. Ocean, 1996, in press.
17. A. M. Davies, 'Numerical problems in simulating tidal flows with a frictional-velocity-dependent eddy viscosity and the influence of stratification', Int. j. numer. methods fluids, 16, 105-131 (1993).
18. J. J. Westerink, R. A. Luettich Jr. and J. C. Muccino, 'Modeling tides in the western North Atlantic using unstructured graded grids', Tellus, 46A, 178-199 (1994).
19. B. J. Noye, 'Finite difference techniques for partial differential equations', in B. J. Noye (ed.), Computational Techniques for Differential Equations, North-Holland, Amsterdam, 1984, pp. 95-354.
20. B. J. Noye and M. Stevens, 'A three-dimensional model of tidal propagation using transformations and variable grids', in N. S. Heaps (ed.), Three-Dimensional Coastal Ocean Models, CES Vol. 4, AGU, Washington, DC, 1987, pp. 41-69.
21. A. M. Davies, 'On the accuracy of finite difference and modal methods for computing tidal and wind waves current profiles', Int. j. numer. methods fluids, 12, 101-124 (1991).
22. K. W. Bowden and S. R. Ferguson, 'Variations with height of the turbulence in a tidally induced bottom boundary layer', in J. C. J. Nihoul (ed.), Marine Turbulence, Proc. 11th Liege Colloq. on Ocean Hydrodynamics, EOS Vol. 28, Elsevier, Amsterdam, 1980, pp. 259-286.
23. A. M. Davies, 'A bottom boundary layer resolving three-dimensional tidal model: a sensitivity study of eddy viscosity formulation', J. Phys. Oceanogr., 23, 1437-1453 (1993).
24. A. M. Davies and J. Aldridge, 'A numerical model study of parameters influencing tidal currents in the Irish Sea', J. Geophys. Res., 98, 7049-7067 (1993).
25. A. M. Davies, 'On the importance of time varying eddy viscosity in generating higher tidal harmonics', J. Geophys. Res., 95, 20,287-20,312 (1990).
26. 2v user's manual. 2D vertical hydrodynamic model for river and tidal analysis. Part I - Flow model', OGI-CCALMR Software Documentation Series SDS7, 93- 3, Oregon Graduate Institute, Portland, OR, 1993.
27. I. P. E. Kinmark, 'The shallow water equations: formulation, analysis and application', in C. A. Brebia and S. A. Orszag (eds), Lecture Notes in Engineering, Vol. 15, Springer, Berlin, 1985.
28. A. M. Davies and J. Lawrence, 'Modelling the non-linear interaction of wind and tide: its influence on current profiles', Int. j. numer. methods fluids, 18, 163-188 (1994).
29. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C, Cambridge University Press, Cambridge, 1988.
30. R. A. Luettich Jr. and J. J. Westerink, 'A solution for the vertical variation of stress, rather than velocity, in a three-dimensional circulation model', Int. j. numer. methods fluids, 12, 911-928 (1991).
31. R. A. Luettich Jr., S. Hu and J. J. Westerink, 'Development of the direct stress solution technique for three-dimensional hydrodynamic models using finite elements', Int. j. numer. methods fluids, 19, 295-319 (1994).
32. J. J. Westerink, J. C. Muccino and R. A. Luettich Jr., 'Resolution requirements for a tidal model of the western North Atlantic and the Gulf of Mexico', Proc. Int. Conf. on Computational Methods in Water Resources IX, Elsevier, Amsterdam, 1992, pp. 667-674.
33. J. J. Westerink, R. A. Luettich Jr. and S. C. Hagen, 'Meshing requirements for large scale coastal ocean tidal models', Proc. Int. Conf. on Computational Methods in Water Resources X, Kluwer, Dordrecht, 1994, pp. 1323-1330.