In Section 12-3, we showed that the unsteady flow in open channels is described by a set of hyperbolic partial differential equations. These equations describe the conservation of mass and momentum in terms of the partial derivatives of dependent variables: flow velocity, V, and flow depth, y. However, for practical applications, we need to know the value of these variables instead of the values of their derivatives. Therefore, we integrate the governing equations. Because of the presence of nonlinear terms, a closed-form solution of these equations is not available, except for very simplified cases. Therefore, they are integrated numerically for which several numerical methods have been presented.
In this chapter, we introduce the method of characteristics and discuss necessary boundary and initial conditions for the numerical solution of governing equations. Various available numerical methods are presented and their advantages and disadvantages are briefly discussed.
KeywordsNegative Characteristic Open Channel Flow Riemann Invariant Venant Equation Characteristic Grid
Unable to display preview. Download preview PDF.
- Abbott, M. B., 1966, An Introduction to the Method of Characteristics, Thames and Hudson, London, and American Elsevier, New York, NY.Google Scholar
- Abbott, M. B., 1975, “Method of Characteristics,” Chapter 3 and ”Weak Solu-tion of the equations of Open Channel Flow,” Chapter 7 of Unsteady Open Channel Flow, (Mahmood, K., and Yevjevich, V. eds.), Water Resources Publications, Fort Collins, CO.Google Scholar
- Abbott, M. B., and Verwey, A., 1970, “Four-Point Method of Characteristics,” Jour. Hyd. Div., Amer. Soc. Civ. Engrs., vol 96, Dec., pp. 2549-2564.Google Scholar
- Amein, M., and Fang, C. S., 1970, “Implicit Flood Routing in Natural Channels,” Jour. Hyd. Div., Amer. Soc. Civ. Engrs., vol. 96, Dec., pp. 2481-2500.Google Scholar
- Baker, J. A., 1983, Finite-Element Computational Fluid Dynamics, McGraw-Hill, New York, NY.Google Scholar
- Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., 1988, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, NY.Google Scholar
- Chaudhry, M. H., 1987, Applied Hydraulic Transients, 2nd ed., Van Nostrand Reinhold, New York, NY. Google Scholar
- Craya, A., 1946, “Calcul graphique des regimes variables dans les canaux,” La Houille Blanche, no. 1, Nov. 1945-Jan 1946, pp. 79-138, and no. 2, Mar 1946, pp. 117-130.Google Scholar
- Cunge, J., Holly, F. M., and Verwey, A., 1980, Practical Aspects of Computa-tional River Hydraulics, Pitman, London.Google Scholar
- Fread, D. L., and Harbaugh, T. E., 1973, “Transient Simulation of Breached Earth Dams,” Jour. Hyd. Div., Amer. Soc. Civil Engrs., Jan., pp. 139-154.Google Scholar
- Isaacson, E., Stoker, J. J., and Troesch, B. A., 1954, “Numerical Solution of Flood Prediction and River Regulation Problems (Ohio-Mississippi Floods),” Report II, Inst. Math. Sci. Rept. IMM-NYU-205, New York University.Google Scholar
- Lai, C., 1986, “Numerical Modeling of Unsteady Open-Channel Flow,” in Ad-vances in Hydroscience, vol. 14, Academic Press, New York., pp. 161-333.Google Scholar
- Leendertse, J. J., 1967, “Aspects of a Computational Model for Long Period Water-Wave Propagation,”Memo RM-5294-PR, Rand Corporation, May.Google Scholar
- Liggett, J. A., 1984, “The Boundary Element Method - Some Fluid Applications,” in Multi-Dimensional Fluid Transients, (Chaudhry, M. H., and Martin, C. S. eds.), Amer. Soc. Mech. Engrs., Dec., New York, NY, pp. 1-8.Google Scholar
- Massau, J., 1889, “L’integration graphique and Appendice au memoire sur l’integration graphique,” Assoc. des Ingenieurs sortis des Ecoles Speciales de Gand, Belgium, Annales, vol. 12, pp. 185-444.Google Scholar
- Price, R. K., 1974, “Comparison of Four Numerical Flood Routing Methods,” Jour. Hyd. Div., Amer. Soc. Civ. Engrs., vol. 100, July, pp. 879-899.Google Scholar
- Strelkoff, T., 1970, “Numerical Solution of St. Venant Equations,” Jour. Hyd. Div., Amer. Soc. Civ. Engrs., vol. 96, January, pp. 223-252. Google Scholar
- Terzidis, G., and Strelkoff, T., 1970, “Computation of Open Channel Surges and Shocks,” Jour. Hyd. Div., Amer. Soc. Civ. Engrs., vol. 96, Dec., pp. 2581-2610.Google Scholar