Summary
A deterministic model to simulate stormwater runoff from impervious surfaces is presented. The surface runoff model is based on a one dimensional, variable width, kinetmatic wave approximation. Resistance to flow is described with the Manning equation for turbulent flow.
A Galerkin finite element formulation utilizing linear, quadratic and cubic Lagrangian elements is presented for the spatial discretization of the kinematic runoff equations. The temporal discretization is based on a linear time variation which includes both explicit and implicit time marching algorithms, depending on the value of the time weighting parameter. The implicit algorithm results in a system of nonlinear equations which are solved using a modified Newton-Raphson iteration scheme. Initial estimates to the solution are generated with a linear finite difference procedure.
A method to estimate a suitable computational time step size based on the Courant condition is presented. Simulation results are compared with the experimental data of Izzard (1946) and conclusions based on these results are presented.
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References
Blandford, G.E., Peters, N., II and Meadows, M.E. (1983), Development of Models for Simulating Stormwater Runoff from Surface Coal Mined Lands - Finite Element Simulation of Overland Flow, Vol. II, U.S. Department of the Interior, Office of Surface Mining, Report No. G511213, 161 pp.
Hughes, T.J.R. (1977), “Unconditionally Stable Algorithms for Nonlinear Heat Conduction,” Comp. Meth. Mech. Engrg., Vol. 10, pp. 135–139.
Izzard, C.F. (1946), “Hydraulics of Runoff from Developed Surfaces,” Highway Res. Board, Proceedings 26th Annual Meeting, pp. 129–150.
Jayawardena, A.W. and White, J.K. (1977), “A Finite Element Distributed Catchment Model, I. Analytical Basis,” J. of Hydrology, Vol. 42, pp. 231–249.
Overton, D.E. and Meadows, M.E. (1976), Stormwater Modeling, Academic Press, New York.
Ross, B.B., Contractor, D.N. and Shanholtz, V. (1979), “A Finite Element Model of Overland and Channel Flow for Assessing the Hydrologic Impact of Land-Use Change,” J. of Hydrology, Vol. 41, pp. 11–30.
Taylor, R.L. (1977), in O.C. Zienkiewicz, The Finite Element Method, Third Edition, McGraw-Hill, New York, Chapter 24.
Viessman, W. Jr., Knapp, J.W., Lewis, G.L. and Harbaugh, T.E. (1977), Introduction to Hydrology, Second Edition, Harper and Row, New York.
Woolhiser, D.A. and Liggett, J.A. (1967), “Unsteady One-Dimensional Flow Over a Plane - The Rising Hydrograph,” Water Resources Res., Vol. 3, No. 3, pp. 753–771.
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© 1984 Springer-Verlag Berlin Heidelberg
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Blandford, G.E., Meadows, M.E. (1984). Finite Element Simulation of Kinematic Surface Runoff. In: Laible, J.P., Brebbia, C.A., Gray, W., Pinder, G. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11744-6_14
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DOI: https://doi.org/10.1007/978-3-662-11744-6_14
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