Tidal Model Using Method of Characteristics
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 118, Issue 3
Abstract
A new numerical technique is presented based on the method of characteristics for the calculation of tidal elevations and currents, both in large sea areas and in coastal regions. Integration of the equations describing two‐dimensional tidal flow is carried out along specific lines, the so‐called bicharacteristics, resulting, thereby, in an explicit finite difference solution scheme that is proven to be second‐order accurate both in space and time. This kind of integration allows the nonlinear convection and, also, the horizontal diffusion terms to be properly treated. This is important because these terms are responsible for the generation of eddies and other circulatory effects inside narrow‐entranced harbors. The validity of the new model is tested against a number of simple analytical cases and two engineering studies for which observational data are available for comparison.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1966). An introduction to the method of characteristics. Elsevier, New York, N.Y.
2.
Benque, J. P., Cunge, J. A., Feuillet, J., Hauguel, A., and Holly, F. M., Jr. (1982). “New method for tidal current computation.” J. Wtrwy., Port, Coast., Oc. Engrg. Div., ASCE, 108(3), 396–417.
3.
Butler, D. S. (1960). “The numerical solution of hyperbolic systems of partial differential equations in three independent variables.” Proc. of the Royal Society, A225, 232–252.
4.
Daubert, A., and Graffe, M. D. (1967). “Quelques aspects des ecoulements Presque horizontaux a deux dimensions en plan et non permanents. Application aux estuaires.” Houille Blanche, 8, 847(in French).
5.
Dronkers, J. J. (1964). Tidal computations in rivers and coastal waters. North Holland Publishers, Amsterdam, the Netherlands.
6.
Falconer, R. A. (1980). “Numerical modelling of tidal circulation in harbors.” J. Wtrwy., Port, Coast., and Oc. Engrg. Div., ASCE, 106(1), 31–48.
7.
Falconer, R. A. (1985). “Residual currents in Port Talbot Harbour: A mathematical model study.” Proc. Inst. Civ. Engrs., London, Part 2, 79, Mar., 33–53.
8.
Fletcher, C. A. J. (1988). Computational techniques for fluid dynamics 1. Springer‐Verlag, New York, N.Y.
9.
Katopodes, N., and Strelkoff, T. (1979). “Two‐dimensional shallow water‐wave models.” J. Engrg. Mech. Div., ASCE, 105(2), 317.
10.
Lai, C. (1976). “Some computational aspects of one‐ and two‐dimensional unsteady flow simulation by the method of characteristics.” Proc. Int. Symp. Unsteady Flow Open Channels, Int. Association Hydr. Res., Newcastle.
11.
Lamb, H. (1932). Hydrodynamics, Cambridge Univ. Press, Cambridge, England, 267.
12.
Lynch, D. R., and Gray, W. G. (1978). “Analytical solutions for computer flow model testing.” J. Hydr. Div., ASCE, 104(10), 1409–1428.
13.
Lynch, D. R., and Gray, W. G. (1979). “A wave equation model for finite element tidal computations.” Comput. Fluids, 7, 207–228.
14.
Matsoukis, P. F. (1980). “The analysis and application of the method of characteristics for simulating long wave propagation in two‐dimensional space, thesis presented to Strathclyde Univ. at Glasgow, U.K., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
15.
Taylor, G. I. (1922). “Tides in the Bristol Channel.” Proc. Cambridge Philosophical Society, 20, 320.
16.
Townson, J. M. (1974). “An application of the method of characteristics to tidal calculations in (x,y,t) space.” J. Hydr. Res., 12(4).
17.
Weare, T. J. (1976). “Instability in tidal flow computational schemes.” J. Hydr. Div., ASCE, 102(5), 569–580.
18.
Weare, T. J. (1979). “Errors arising from irregular boundaries in ADI solutions of the shallow water equation.” Int. J. Numer. Methods in Engrg., 14, 921–931.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 118 • Issue 3 • May 1992
Pages: 233 - 248
Copyright
Copyright © 1992 ASCE.
History
Published online: May 1, 1992
Published in print: May 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.