Oscillation‐Free Solution of Shallow Water Equations for Nonstaggered Grid
Publication: Journal of Hydraulic Engineering
Volume 119, Issue 10
Abstract
This paper contains a description of the method for the solution of the shallow water equations on nonstaggered grid points. The shallow water equations are split up in relation to the independent variables and as well as physical processes. Such a procedure reduces a solution of two‐dimensional problem to the solution of a number of one‐dimensional problems. A spatial discretization of these one‐dimensional equations is based on the finite difference method and the finite element method with the use of the nonstaggered numerical grid. The applied schemes of approximation ensure a smooth solution without oscillations of type “2Δ.”
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References
1.
Benqué, J. P., Cunge, J. A.Feuillet, J., Haunguel, A., and Holly, F. M. Jr. (1982). “New method for tidal current computation.” J. Wtwys., Port, Coast. and Oc. Div., ASCE, 108(3), 396–417.
2.
Cunge, J., Holly, F. M. Jr., and Verwey, A. (1980). Practical aspect of computational river hydraulics. Pitman, London, England.
3.
Fletcher, C. A. J. (1991). Computational techniques for fluid dynamics. vol. I and II, Springer‐Verlag, Berlin, Germany.
4.
Liggett, J. A., and Cunge, J. A. (1975). “Numerical methods of solution of the unsteady flow equations.” Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., vol. 1, Water Res. Publ., Fort Collins, Colo., 89–182.
5.
Marchuk, G. I. (1985). Mathematical modelling of environmental problems. Polish Ed., Panstwowe Wydawnictwo Naukowe, Warsaw, Poland.
6.
Stelling, G. S. (1984). “On the construction of computational methods for shallow water flow problems.” Rijkwaterstaat Comunications, 35, The Hague, The Netherlands.
7.
Szymkiewicz, R. (1992). “Mathematical model of storm surge in Vistula Lagoon, Poland.” Coastal Engrg., 16, Amsterdam, The Netherlands, 181–203.
8.
Usseglio‐Polatera, J. M., and Chenin‐Mordojovich, M. I. (1988). “Fractional steps and process splitting methods for industrial codes.” Computational methods in water resources, vol. 2: numerical methods for transport and hydrologic processes, Elsevier, Amsterdam, The Netherlands, 167–172.
9.
Zienkiewicz, O. (1972). The finite elements method. Polish Ed., Arkady, Warsaw, Poland.
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Copyright © 1993 American Society of Civil Engineers.
History
Received: Jan 14, 1992
Published online: Oct 1, 1993
Published in print: Oct 1993
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