Model for Flood Propagation on Initially Dry Land
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 7
Abstract
A model is presented for the simulation of shallow water flow and, specifically, flood waves propagating on a dry bed. The governing equations are transformed to an equivalent system valid on a deforming coordinate system and are solved by a dissipative finiteelement technique. A second‐order difference scheme is employed for the integration in time. The implicit nonlinear equations resulting from the weak formulations are solved by the Newton‐Raphson method, and the set of linear algebraic equations generated is solved by a frontal algorithm. A deforming grid generation scheme is introduced in the dissipative finite‐element formulation to account for the effects of the propagating or receding wave fronts on dry land. The accuracy and stability of the model is examined by comparing the model results with observed data from an experimental field test. Results of trial runs for the simulation of overland flow are also presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Akanbi, A. A. (1986). “Hydrodynamic modeling of two‐dimensional overland flow,” thesis presented to the University of Michigan, at Ann Arbor, Mich., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Al‐Mashidani, G., and C. Taylor (1974). “Finite element solution of the shallow water equations—surface run‐off.” Proc., Finite Element Methods in Flow Problems, University of Wales, Swansea, U.K. 385–398.
3.
Bonnerot, R., and Jamet, P. (1977). “Numerical computation of the free Boundary for the two‐dimensional Stefan problem by space—time finite elements.” J. Comput. Phys., 25, 163.
4.
Cunge, J. A., Holly, F. M., Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics. Pitman Pub., London, U.K.
5.
Davis, F. S., and Flaherty, J. E. (1982). “An adaptive finite element method for initial‐boundary value problems for partial differential equations.” J. Sci. Stat. Comput., SIAM, 3(1), 6–27.
6.
Gelinas, R. J., Doss, S. K., and Miller, K. (1981). “The moving finite element method: application to general partial differential equations with multiple large gradients.” J. Comp. Phy., 40, 202–249.
7.
Katopodes, N. D. (1980). “A finite element model for open‐channel flow near critical conditions.” Proc. 3rd Int. Conf. on Finite Elements on Water Resources, Oxford, Miss., 5.37–5.46.
8.
Katopodes, N. D. (1984). “A dissipative Galerkin scheme for open‐channel flow.” J. Hydr. Engrg., ASCE, 110(HY4) 450–466.
9.
Katopodes, N. D. (1985). “Analysis of transient flow through broken levees.” Proc. 4th Int. Conf. on Refined Flow Modeling, Iowa City, Iowa.
10.
Katopodes, N. D., and Schamber, D. R. (1983). “Applicability of dam‐break flood wave models.” J. Hydr. Engrg., ASCE, 109(5) 702–721.
11.
Katopodes, N. D., and Strelkoff, T. (1978). “Computing two‐dimensional dambreak flood waves.” J. Hydr. Div., ASCE, 104(HY9), 1269–1288.
12.
Lynch, D. R. (1982). “Unified approach to simulation on deforming elements with application to phase change problems.” J. Comp. Phys., 47(3), 387–411.
13.
Lynch, D. R., and Gray, W. G. (1980). “Finite element simulation of flows in deforming regions.” J. Comput. Phys., 135–153.
14.
Miller, K. (1981). “Moving finite elements: II.” J. Num. Anal., SIAM, 108(6), 1033–1057.
15.
Miller, K., and Miller, R. N. (1981). “Moving finite elements: I.” J. Num. Anal., SIAM, 108(6) 1019–1032.
16.
Mueller, A. C., and Carey, G. F. (1983). “Moving meshes in time dependent calculations.” Scientific computing, R. Stepleton, et al., eds., IMAC/North‐Holland Publishing Co., 37–42.
17.
Pinder, G. F., and Gray, W. G.U977). Finite element simulation in surface and subsurface hydrology. Academic Press, New York, N.Y.
18.
Roth, R. L., et al. (1979). “Data for border irrigation models.” Trans., ASAE, 157–161.
19.
Smith, R. E., (1972). “Border irrigation advance and ephemeral flood waves.” J. Irrig., and Drain. Div., ASCE, 98(IR2), 289–306.
20.
Vasiliev, O. F. (1970). “Numerical solution of nonlinear problems of unsteady flows in open channels.” Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics, Berkeley, Calif.
21.
Wang, J. D., and Connor, J. J. (1975). “Mathematical modeling of near coastal circulation,” Report #200, Ralphs M. Parsons Lab. for Water Resources and Hydrodynamics.
22.
Whitham, G. B. (1955). “The effects of the hydraulic resistance in the dam‐break problem.” Proc., R. Soc. of London Ser. A, 227, 399–407.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 7 • July 1988
Pages: 689 - 706
Copyright
Copyright © 1988 ASCE.
History
Published online: Jul 1, 1988
Published in print: Jul 1988
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.