Finite Difference Formulations of Kinematic Equations
Publication: Journal of Hydraulic Engineering
Volume 121, Issue 5
Abstract
The accuracy of finite-difference solutions to the kinematic equations for runoff modeling is affected when numerical diffusion or instability occurs. The effect of grid ratio and the spatial and temporal weighting coefficients in four-point difference schemes are discussed. Inaccuracies resulting from numerical diffusion are related to the temporal weighting coefficient, and a variable coefficient is suggested to eliminate uncontrolled numerical diffusion. The occurrence of parasitic waves is investigated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Brakensiek, D. L.(1967). “Kinematic flood routing.”Trans. ASAE, 10(3), 340–343.
2.
Constantinides, C. A. (1982). “Two-dimensional kinematic modelling of the rainfall-runoff process.”Rep. 1/1982, Dept. of Civ. Engineering, Water Systems Res. Programme, Univ. of the Witwatersrand, Johannesburg, Republic of South Africa.
3.
Courant, R., Friedrichs, K. O., and Lewy, H. (1928). “Uber die partiellen Differentialgleichungen der Mathematishcen Physik.”Mathematical Ann., London, England, Vol. 100 (in German).
4.
Cunge, J.(1969). “On the subject of a flood propagation computation method (Muskingum method).”J. Hydr. Res., 7(2), 205–230.
5.
Holden, A. P., and Stephenson, D.(1988). “Improved four-point solution of the kinematic equations.”J. Hydr. Res., 26(4), 413–423.
6.
Huang, Y. H.(1978). “Channel routing by finite-difference method.”J. Hydr. Div., ASCE, 104(10), 1379–1393.
7.
Liggett, J. A., and Woolhiser, D. A. (1967). “Finite-difference solutions of the shallow-water equations.”J. Engrg. Mech. Div., ASCE, 93(2), 39–71.
8.
Lyn, D. A., and Goodwin, P.(1987). “Stability of a general Preissmann scheme.”J. Hydr. Engrg., ASCE, 113(1), 16–28.
9.
Morgali, J. R.(1970). “Laminar and turbulent overland flow hydrographs.”J. Hydr. Div., ASCE, 96(2), 441–460.
10.
Ponce, V. M., Chen, V. H., and Simons, D. B.(1979). “Unconditional stability in convection computations.”J. Hydr. Div., ASCE, 105(9), 1079–1086.
11.
Ponce, V. M., and Yevjevich, V.(1978). “Muskingum-Cunge method with variable parameters.”J. Hydr. Div., ASCE, 104(12), 1663–1667.
12.
Preissmann, A. (1961). “Propogation des intumescences dans les canaux et les Rivieres.” 1'e Congres de l'Association Francaise de Culcule, Grenoble, France, 433–442 (in French).
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: May 1, 1995
Published in print: May 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.