Velocity-Depth Coupling in Shallow-Water Flows
Publication: Journal of Hydraulic Engineering
Volume 121, Issue 10
Abstract
The two-dimensional shallow-water flow equations are first written in strong conservation form and are used for developing the flow model. In the discretization equations, based on the control volume method, the velocity field is found to be proportional to both the square of the depth and the depth itself. Due to this, none of the existing SIMPLE-like algorithms can be used to deal with the velocity-depth coupling. In this paper, the problem of velocity-depth coupling is studied, and a modified SIMPLE-like algorithm is described to treat it. Several applications of the model have shown that the method is efficient, simple, and has good convergence behavior. Also, a different value for the relaxation factor for depth is found to speed the convergence rate after stable convergence occurs. The results are in good agreement with both experimental observations and theoretical analysis. The method can straightforwardly be extended into unsteady shallow-water flows.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Chow, V. T. (1959). Open-channel hydraulics. McGraw-Hill Book Co., New York, N.Y.
2.
Demirdzic, I. A. (1982). “A finite volume method for computation of fluid flow in complex geometries,” PhD thesis, London Univ., London, England.
3.
Graber, S. D.(1982). “Asymmetric flow in symmetric expansions.”J. Hydr. Engrg. Div., ASCE, 108(10), 1082–1101.
4.
Grubert, J. P.(1976). “Numerical computation of two-dimensional flows.”J. Wtrwy., Harb., and Coast. Engrg. Div., ASCE, 102(1), 11891.
5.
McGuirk, J. J., and Rodi, W.(1978). “A depth-averaged mathematical model for the field of side discharges into open-channel flow.”J. Fluid Mech., 86, 761–781.
6.
Patankar, S. V. (1980). Numerical heat transfer and fluid flow. Hemisphere Publishing Corp., New York, N.Y.
7.
Patankar, S. V.(1981). “A calculation procedure for two-dimensional elliptic situation.”Numerical Heat Transfer, 4, 409–425.
8.
Patankar, S. V., and Spalding, D. B.(1972). “A calculation procedure for heat, mass and momentum transfer in three-dimensional flows.”Int. J. Heat Mass Transfer, 15, 1787–1806.
9.
Ponce, V. M., and Yabusaki, S. B.(1981). “Modeling circulation in depth-averaged flow.”J. Hydr. Engrg. Div., ASCE, 107(11), 1501–1518.
10.
Shimizu, Y., and Itakura, T.(1989). “Calculation of bed variation in alluvial channels.”J. Hydr. Engrg. Div., ASCE, 115(3), 367–384.
11.
Van Doormaal, J. P., and Raithby, G. D.(1984). “Enhancement of the SIMPLE method for prediction incompressible fluid flows.”Numerical Heat Transfer, 7(2), 147–163.
12.
Wenka, T., Valenta, P., and Rodi, W. (1991). “Depth-averaged calculation of flood flows in a river with irregular geometry.”24th IAHR Congr., Int. Assoc. of Hydr. Res. (IAHR), Fort Collins, Colo.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 121 • Issue 10 • October 1995
Pages: 717 - 724
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Oct 1, 1995
Published in print: Oct 1995
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.