Abstract
Much research effort has been directed toward finding numerical solutions to the shallow water equations (see Pritchard, 1971, for a clear derivation of these equations). Although finite difference modelers have enjoyed much success in solving these equations, finite-element modelers have experienced many difficulties in obtaining stable, accurate solutions (Gray, 1980). Recently Lynch and Gray (1979) have reported on a wave equation formulation which seems to provide significant numerical advantages for finite element simulations.
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References
Gray, W.G. (1980) Do finite element models simulate surface flow? Proceedings of the Third International Conference on Finite Elements in Water Resources, pp. 1. 122–1. 136.
Gray, W.G. and D.R. Lynch (1977) Time-stepping schemes for finite element tidal model computations, Advances in Water Resources, 1, 2, 83–95.
Gray, W.G., D.R. Lynch, I. Kinnmark (1982) An explicit model for two-dimensional tidal circulation using isoparametric finite elements: WAVEQ User’s Manual, Princeton University Water Resources Program Report 82-WR-1, 91 pp.
Lynch, D.R. and W.G. Gray (1979) A wave equation model for finite element tidal computations, Computers and Fluids 7, 3, 207–228.
Lynch, D.R. and W.G. Gray (1980) On the analysis of accuracy for two-equation transient problems, Intl. J. Numer. Meth. in Engrg., 15, 55–62.
Pritchard, D.W. (1971) Two-dimensional models, in G.H. Ward and W.H. Espery, eds., Estuarine Modeling: An Assessment, 1/PB2O6–807, Water Quality Office, U.S. Environmental Protection Agency.
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© 1982 Springer-Verlag Berlin Heidelberg
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Kinnmark, I.P.E., Gray, W.G. (1982). Time-Weighting of the Momentum Equation in Explicit Wave Equation Models of Surface Water Flow. In: Holz, K.P., Meissner, U., Zielke, W., Brebbia, C.A., Pinder, G., Gray, W. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02348-8_28
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DOI: https://doi.org/10.1007/978-3-662-02348-8_28
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