Great Lakes River‐Estuary Hydrodynamic Finite Element Model
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 11
Abstract
A deterministic hydrodynamic model for simulating the water flow in a well‐mixed freshwater estuary is developed for the purpose of long‐term environmental flow simulation. The hydrodynamic simulation is based on solving the shallow‐water equations using the finite element method. The Galerkin approach to the finite element method is applied to approximate the spatial variables. A leapfrog scheme is used to evaluate the temporal terms of the unsteady‐state hydrodynamic equation. The combined numerical scheme has proven to be an efficient and conditionally stable method suitable for long‐term, real‐time simulation. The numerical method is verified with a set of analytical solutions for various geometric channel configurations. In addition, the model has been applied in the lower Green Bay and Fox River system in Lake Michigan using an extensive set of field data measured specifically for calibration and confirmation purposes.
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References
1.
Gray, W. G. (1982). “Some inadequacies of finite‐element models as simulators of wo‐dimensional circulation.” Adv. Water Resour., 5(9), 171–177.
2.
Gray, W. G., and Lynch, D. R. (1977). “Time‐stepping schemes for finite element tidal model computations.” Adv. Water Resour., 1(2), 83–95.
3.
Gray, W. G., and Lynch, D. R. (1979). “On the control of noise in finite element tidal computation: A semi‐implicit approach.” Comput. Fluids, 7(1), 47–67.
4.
Gresho, P. M., and Lee, R. L. (1979). “Don't suppress the wiggles—They're telling you something.” Finite element methods for convection dominated flows, T. J. R. Hughes, ed., AMD Vol. 34, ASME, New York, N.Y.
5.
Grotkop, G. (1973). “Finite element analysis of long‐period water waves.” Comput. ethods Appl. Mech. Engrg., 2, 147–159.
6.
Ippen, A. T., and Goda, Y. (1963). “Wave induced oscillations in harbors: The solution for a rectangular harbor connected to the open sea.” Report No. 59, Hydrodynamic Laboratory, MIT, Cambridge, Mass.
7.
Kawahara, M. (1977). “Steady and unsteady finite element analysis of incompressible viscous fluid.” Chuo University Report, Japan.
8.
King, I. P., Norton, W. R., and Iceman, K. R. (1975). “A finite element solution for two‐dimensional stratified flow problems.” Finite elements in fluids, 1, R. H. Gallagher, J. T. Oden, C. Taylor, and O. C. Zienkiewicz, eds., John Wiley and Sons, London, U.K.
9.
Leendertse, J. J. (1967). “Aspects of a computational model for long‐period water‐wave propagation.” Memorandum RM‐5295‐PR, Rand Corporation, Santa Monica, Calif.
10.
Leendertse, J. J. (1970). “A water‐quality simulation model for well‐mixed estuaries and coastal seas: Vol. I. Principles of computation.” Memorandum RM‐6230‐RC, Rand Corporation, Santa Monica, Calif.
11.
Leonard, B. P. (1979). “A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation.” Finite element methods for convection dominated flows, T. J. R. Hughes, ed., AMD Vol. 34, ASME, New York, N.Y.
12.
Lynch, D. R. (1978). “Finite element solution of the shallow water equations,” thesis presented to Princeton University, at Princeton, N.J., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Lynch, D. R., and Gray, W. G. “A wave equation model for finite element tidal computations.” Comput. Fluids, 7(3), 207–228.
14.
Niemeyer, G. (1979). “Efficient simulation of nonlinear steady flow.” J. Hydr. Div., ASCE, 105(3), 185–195.
15.
Partridge, P. W., and Brebbia, C. A. (1976). “Quadratic finite elements in shallow water problems.” J. Hydr. Div., ASCE, 102(9), 1299–1313.
16.
Platzman, G. W. (1981). “Some response characteristics of finite‐element tidal models.” J. Computat. Phys., 40, 36–63.
17.
Pinder, G. F., and Gray, W. G. (1977). Finite element simulation in surface and subsurface hydrology. Academic Press, New York, N.Y.
18.
Pritchard, D. W. (1971). “Two dimensional models.” Estuarine modelling: An assessment. G. H. Ward and W. H. Espey, eds., Environmental Protection Agency, Water Quality Office, NTIS Publication No. PB 206‐807, Washington, D.C.
19.
Roach, P. J. (1976). Computation fluid dynamics. Hermosa Publishers, Albuquerque, N.M.
20.
Taylor, C., and Davis, J. M. (1975). “Tidal propagation and dispersion in estuaries.” Finite element in fluids, 1, R. H. Gallagher, J. H. Oden, C. Taylor, and O. C. Zienkiewicz, eds., John Wiley and Sons, London, U.K.
21.
Walters, R. A., and Cheng, R. T. (1980). “Accuracy of an estuarine hydrodynamic model using smooth elements.” Water Resour. Res., 16(1), 187–195.
22.
Wang, J. D., and Connor, J. J. (1975). “Mathematical modelling of near coastal circulation.” Report No. 200. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, Mass.
23.
Zienkiewicz, O. C. (1977). The finite element method in engineering science. McGraw‐Hill, London, U.K.
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Copyright © 1991 ASCE.
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Published online: Nov 1, 1991
Published in print: Nov 1991
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