TECHNICAL NOTES
Nov 1, 1997

Analytic Benchmark Solutions for Open-Channel Flows

Publication: Journal of Hydraulic Engineering
Volume 123, Issue 11

Abstract

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

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References

1.
Bakhmeteff, B. A. (1932). Hydraulics of open channels. McGraw-Hill, Inc., London, England.
2.
Bresse, J. A. C. (1860). “Cours de mécanique appliquée.” 2de partie, Hydraulique, Mallet-Bachelier, Paris, France (in French).
3.
Chow, V. T.(1955). “Integrating the equation of gradually varied flow.”Proc., Am. Soc. Engrs., 81, 1–32.
4.
Chow, V. T. (1959). Open channel hydraulics. McGraw-Hill, Inc., London, England.
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Cunge, J. A. (1989). “Review of recent developments in river modelling.”Proc., Int. Conf. on Hydr. and Envir. Modelling of Coastal, Estuarine and River Waters, Bradford, 1989, Gower Technical, Aldershot, 393–410.
6.
Dee, D. (1994). Standard validation document: Definition and guidelines. Delft Hydraulics, The Netherlands.
7.
MacDonald, I. (1996). “Analysis and computation of steady open channel flow,” PhD thesis, Dept. of Mathematics, Univ. of Reading, U.K.
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MacDonald, I., Baines, M. J., Nichols, N. K., and Samuels, P. G. (1995a). “Comparison of some steady state Saint-Venant solvers for some test problems with analytic solutions.”Numer. Analy. Rep. (2/95), Dept. of Mathematics, Univ. of Reading, U.K.
9.
MacDonald, I., Baines, M. J., Nichols, N. K., and Samuels, P. G. (1995b). “A new method for the computation of steady open channel trans-critical flow.”Hydra 2000—Proc., 26th IAHR Congr., London, 1995, Thomas Telford, Ltd., London, England, 561–565.
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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 123Issue 11November 1997
Pages: 1041 - 1045

History

Published online: Nov 1, 1997
Published in print: Nov 1997

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Authors

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I. MacDonald
Dept. of Mathematics, Univ. of Reading, P.O. Box 220, Reading RG6 6AF, U.K.
M. J. Baines
Dept. of Mathematics, Univ. of Reading, P.O. Box 220, Reading RG6 6AF, U.K.
N. K. Nichols
Dept. of Mathematics, Univ. of Reading, P.O. Box 220, Reading RG6 6AF, U.K.
P. G. Samuels
HR Wallingford Ltd., Howbery Park, Wallingford, Oxon OX10 8BA, U.K.

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