Two-Dimensional Simulation of Subcritical Flow at a Combining Junction: Luxury or Necessity?
Publication: Journal of Hydraulic Engineering
Volume 136, Issue 10
Abstract
Classically, in open-channel networks, the flow is numerically approximated by the one-dimensional Saint Venant equations coupled with a junction model. In this study, a comparison between the one-dimensional (1D) and two-dimensional (2D) numerical simulations of subcritical flow in open-channel networks is presented and completely described allowing for a full comprehension of the modeling of water flow. For the 1D, the mathematical model used is the 1D Saint Venant equations to find the solution in branches. For junction, various models based on momentum or energy conservation have been developed to relate the flow variables at the junction. These models are of empirical nature due to certain parameters given by experimental results and moreover they often present a reduced field of validity. In contrast, for the 2D simulation, the junction is discretized into triangular cells and we simply apply the 2D Saint Venant equations, which are solved by a second-order finite-volume method. In order to give an answer to the question of luxury or necessity of the 2D approach, the 1D and 2D numerical results for steady flow are compared to existing experimental data.
Get full access to this article
View all available purchase options and get full access to this article.
References
Akan, A. O., and Yen, B. C. (1981). “Diffusion wave flood routing in channel network.” J. Hydr. Div., 107(6), 719–723.
Best, J. L., and Reid, I. (1984). “Separation zone at open-channel junctions.” J. Hydraul. Eng., 110(11), 1588–1594.
Cockburn, B., and Shu, C. W. (1998). “The Runge-Kutta discontinuous Galerkin finite element method for conservation laws V: Multidimensional systems.” J. Comput. Phys., 141, 199–224.
Frazao, S. S., and Guinot, V.(2007). “An eigenvector-based linear reconstruction scheme for the shallow-water equations on two-dimentional instructured meshes.” Int. J. Numer. Methods Fluids, 53(1), 23–55.
Garcia-Navarro, P., and Saviron, J. (1992). “McCormack’s method for the numerical simulation of one-dimensional discontinuous unsteady open channel flow.” J. Hydraul. Res., 30, 95–105.
Gurram, S. K. (1994). “A study of subcritical and transitional combining flow in open channel junctions.” Ph.D. thesis, Banaras Hindu Univ., Varanasi, India,.
Gurram, S. K., Karki, K. S., and Hager, W. H. (1997). “Subcritical junction flow.” J. Hydraul. Eng., 123(5), 447–455.
Hager, W. H. (1987). “Discussion of ‘Separation zone at open-channel junctions,’ by James. L. Best and Ian Reid.” J. Hydraul. Eng., 113(4), 539–543.
Hirsch, C. (1990). Numerical computation of internal and external flows, computational methods for inviscid and viscous flows, Vol. II, John Wiley & Sons, Chichester, England and New York
Hsu, C. C., Lee, W. J., and Chang, C. H. (1998a). “Subcritical open channel junction flow.” J. Hydraul. Eng., 124(8), 847–855.
Hsu, C. C., Wu, F. S., and Lee, W. J. (1998b). “Flow at 90° equal-width open-channel junction.” J. Hydraul. Eng., 124(2), 186–191.
Modi, P. N., Ariel, P. D., and Dandekar, M. M. (1981). “Conformal mapping for channel junction flow.” J. Hydr. Div., 107(12), 1713–1733.
Ramamurthy, A. S., Carballada, L. B., and Tran, D. M. (1988). “Combining open channel flow at right angled junctions.” J. Hydraul. Eng., 114(12), 1449–1460.
Roe, P. L. (1981). “Approximate Riemann solvers, parameter vectors, and difference schemes.” J. Comput. Phys., 43, 357–372.
Shabayek, S., Steffler, P., and Hicks, F. (2002). “Dynamic model for subcritical combining flows in channel junctions.” J. Hydraul. Eng., 128(9), 821–828.
Taylor, E. H. (1944). “Flow characteristics at rectangular open-channel junctions.” Trans. Am. Soc. Civ. Eng., 109, 893–912.
Webber, N. B., and Greated, C. A. (1966). “An investigation of flow behaviour at the junction of rectangular channels.” Proc., Institute Civil Engineers, Vol. 34, London, pp. 321–334, 321–334.
Yen, B. C. (1979). Unsteady flow mathematical modelling techniques: Modelling of rivers, H. W. Shen, ed., Vol. 13, Wiley-Interscience, New York, 13–33.
Yen, B. C., and Osman, A. (1976). “Flood routing through river junctions.” ASCE Rivers’76, Vol. 1, ASCE, New York, 212–231.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Sep 11, 2007
Accepted: Mar 19, 2010
Published online: Mar 27, 2010
Published in print: Oct 2010
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.