Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing
Publication: Journal of Hydrologic Engineering
Volume 8, Issue 5
Abstract
Using a reference Froude number, a nonlinear convection-diffusion equation was derived from the Saint-Venant equations of continuity and momentum, and was solved by a mixing-cell method. The method involves discretizing the nonlinear diffusion equation in space and transforming it to a first-order nonlinear ordinary differential equation where the optimal space interval is obtained to be the same as the characteristic reach length. The nonlinear ordinary differential equation was solved by the fourth-order Runge-Kutta method. The method was tested with numerical examples, and compared with the looped-rating Muskingum-Cunge model and a lambda scheme. The outflow hydrographs produced by this method were of comparable accuracy.
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References
Akan, A. O., and Yen, B. C. (1977). “A nonlinear diffusion-wave model for unsteady open-channel flow.” Proc., 17th Congress, International Association for Hydraulic Research, Delft, The Netherlands, 2, 181–190.
Akan, A. O., and Yen, B. C.(1981). “Diffusion-wave flood routing in channel networks.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(6), 719–732.
Bajracharya, K., and Barry, D. A.(1997). “Accuracy criteria for linearised diffusion wave flood routing.” J. Hydrol., 195(1-4), 200.
Chow, V. T. (1964). Handbook of applied hydrology, McGraw-Hill, New York.
Dooge, J. C. (1973). “Linear theory of hydrologic systems.” U.S. Dept. of Agriculture Technical Bulletin 1468, Washington, D.C.
Dooge, J. C., Kundzwicz, Z. W., and Napiorkowski, J. P.(1983). “On backwater effects in linear diffusion flood routing.” Hydrol. Sci. J., 28(3), 391–402.
Fennema, R. J., and Chaudhry, M. H.(1986). “Second-order numerical schemes for unsteady free-surface flows with shocks.” Water Resour. Res., 22(13), 1923–1930.
Gonwa, W. S., and Kavvas, M. L.(1986). “A modified diffusion wave equation for flood propagation in trapezoidal channels.” J. Hydrol., 83, 119–136.
Govindaraju, R. S., Jones, S. E., and Kavvas, M. L.(1988). “On the diffusion wave modeling for overland flow. 1. Solution for steep slopes.” Water Resour. Res., 24(5), 734–744.
Hayami, S. (1951). “On the propagation of flood waves.” Disaster Pre-vention Research Institute Bulletin 1, Kyoto Univ., Kyoto, Japan.
Keefer, T. H.(1976). “Comparison of linear systems and finite difference flow routing techniques.” Water Resour. Res., 12(5), 997–1006.
Keefer, T. N., and McQuivey, R. S.(1974). “Multiple linearization flow routing model.” J. Hydraul. Div., Am. Soc. Civ. Eng., 100(7), 1031–1046.
Miller, W. A., and Cunge, J. A. (1975). “Chapter 5: Simplified equations of unsteady flow.” Unsteady flow in open channels, Vol. 1, K. Mahmood and V. Yevjevich, eds., Water Resources Publications, Fort Collins, Colo., 183–257.
Moretti, G.(1979). “The lambda scheme.” Comput. Fluids, 7, 191–205.
Morris, E. M.(1979). “The effect of the small-slope approximation and lower boundary conditions on solutions of the Saint-Venant equations.” J. Hydrol., 40, 31–47.
Ponce, V. M.(1990). “Generalized diffusion wave equation with inertial effects.” Water Resour. Res., 26(5), 1099–1101.
Ponce, V. M.(1991). “New perspective on the Vedernikov number.” Water Resour. Res., 27(7), 1777–1779.
Ponce, V. M., and Lugo, A.(2001). “Modeling looped ratings in Muskingum-Cunge routing.” J. Hydrologic Eng., 6(2), 119–124.
Ponce, V. M., Simons, D. B., and Li, R.-M.(1978). “Applicability of kinematic and diffusion models.” J. Hydraul. Div., Am. Soc. Civ. Eng., 104(3), 353–360.
Singh, V. P. (1996). Kinematic wave modeling in water resources: Surface water hydrology, Wiley, New York.
Singh, V. P., Wang, G.-T., and Adrian, D. D.(1997). “Flood routing based on diffusion wave equation using mixing cell method.” Hydrolog. Process., 11, 1881–1894.
Sturm, T. W. (2001). Open channel hydraulics, McGraw-Hill, New York.
Sutherland, A. J., and Barnett, A. G.(1972). “Diffusion solutions to flows with upstream control.” J. Hydraul. Div., Am. Soc. Civ. Eng., 98(11), 1969–1982.
Tingsanchali, T., and Manandhar, S. K.(1985). “Analytical diffusion model for flood routing.” J. Hydraul. Eng., 111(3), 435–454.
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Published In
Journal of Hydrologic Engineering
Volume 8 • Issue 5 • September 2003
Pages: 259 - 265
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Jun 4, 2002
Accepted: Jan 21, 2003
Published online: Aug 15, 2003
Published in print: Sep 2003
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