Numerical Simulation of Transcritical Flow in Open Channels
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 9
Abstract
The term transcritical flow denotes the existence of both subcritical and supercritical flow regimes in an open-channel system. It is similar to transonic flow in gas dynamics. Transcritical flow is encountered in many engineering problems of practical interest; irrigation networks, for example, often involve transcritical flow caused by the dynamic operation of hydraulic structures. This paper presents a two-step, predictor-corrector, implicit numerical scheme for simulating transcritical flows of practical interest. The proposed scheme is second-order accurate in time and space and requires inversion of only bidiagonal matrices. It is, therefore, computationally efficient and can readily accommodate hydraulic structures. To suppress spurious oscillations near regions of steep gradients and facilitate the resolution of hydraulic jumps, nonlinear (adaptive) second-difference artificial dissipation terms are added explicitly. The scheme is validated by calculating a series of applications of practical interest. The computed solutions are compared with previously published results and exact solutions where available. It is shown that the proposed scheme is robust and accurate, has reasonable shock-capturing capabilities, and can easily simulate hydraulic structures.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Casier, F., Deconinck, H., and Hirsch, C.(1984). “A class of bidiagonal schemes for solving the Euler equations.”AIAA J., 22(11), 1556–1563.
2.
Cunge, J. A., Holley, F. M. Jr., and Verwey, A. (1980). “Practical aspects of computational river hydraulics.”Rep., Iowa Inst. of Hydr. Res., Iowa City, Iowa.
3.
De St. Venant, B. (1871). “Theorie du mouvement non-permanent des eaux avec application aux crues des riveres et a lintroduction des marees dans leur lit.”Acad. Sci. Comptes Redus, 73, 99.148–154, 273–240 (in French).
4.
Fennema, R. J., and Chaudhry, M. H.(1986). “Explicit numerical schemes for unsteady free-surface flows with shocks.”Water Resour. Res., 22(13), 1923–1930.
5.
Fennema, R. J., and Chaudhry, M. H.(1990). “Explicit methods for 2-D transient free-surface flows.”J. Hydr. Engrg., 116(8), 1013–1034.
6.
Glaister, P.(1993). “Flux difference splitting for open-channel flows.”Int. J. for Numer. Methods in Fluids, 16, 629–654.
7.
Hirsch, C. (1990). “Computational methods for inviscid and viscous flows.”Numerical Computation of Internal and External Flows, Vol. 2, John Wiley & Sons, New York, N.Y.
8.
Holly, F. M. Jr., and Parrish, J. B. (1992). “Dynamic flow simulation in irrigation canals with automatic gate control.”Limited Distribution Rep., no. 196, Iowa Inst. Hydr. Res., Univ. of Iowa, Iowa City, Iowa.
9.
Jameson, A., Schmidt, W., and Turkel, E. (1981). “Numerical simulation of the Euler equations by finite volume methods using Runge Kutta time stepping schemes.”Proc., AIAA Fifth Computational Fluid Dynamics Conf., Am. Inst. of Aeronautics and Astronautics,
10.
Meselhe, E. A. (1994). “Numerical simulation of transcritical flow in open channels,” PhD thesis, Civ. and Envir. Engrg., Iowa Inst. of Hydr. Res., Univ. of Iowa, Iowa City, Iowa.
11.
Navarro, G. P., Alcrudo, F., and Saviron, J. M.(1992). “1-D open-channel flow simulation using TVD-MacCormack scheme.”J. Hydr. Engrg., ASCE, 118(10), 1359–1372.
12.
Pulliam, T. H.(1986). “Artificial dissipation models for the Euler equations.”AIAA J., 24(12), 1931–1940.
13.
Pulliam, T. H., and Steger, J. L. (1985). “Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms.”Proc., AIAA 23rd Aerospace Sciences Meeting, Am. Inst. of Aeronautics and Astronautics.
14.
Savic, L. J., and Holly, F. M. Jr.(1993). “Dambreak flood waves computed by modified Godunov method.”J. Hydr. Res., 31(2), 187–204.
15.
Yang, J. Y., Hsu, C. A., and Chang, S. H.(1993). “Computation of free surface flows.”J. Hydr. Res., 31(1), 19–34.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 9 • September 1997
Pages: 774 - 783
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Sep 1, 1997
Published in print: Sep 1997
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.