Research Article
Apr 1967
Difference Solutions of the Shallow-Water Equation
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 93, Issue 2
Abstract
The quasi-linear partial differential equations known as the shallow-water equations describe the flow of water in open channels or over sloping planes (overland flow). Because no analytic solution exists for these equations, finite-difference methods must be used to obtain solutions. Formulation of finite-difference schemes involves consideration of the convergence of the finite-difference solutions to the true solution of the equation. A theoretical examination of the approximation of several difference operators, both implicit and explicit, is presented and the stability of these schemes is examined empirically for flow over a plane with critical depth downstream boundary condition and a zero inflow upstream boundary condition. A finite-difference scheme based on the method of characteristics was found to be satisfactory in many cases. Explicit methods were found to be not suitable for this problem except in some special cases.
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Published In
Journal of the Engineering Mechanics Division
Volume 93 • Issue 2 • April 1967
Pages: 39 - 72
Copyright
© 1967 American Society of Civil Engineers.
History
Published in print: Apr 1967
Published online: Feb 3, 2021
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Authors
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James A. Liggett, AM.ASCE
Assoc. Prof. of Civ. Engrg., Cornell Univ., Ithaca, N. Y.
David A. Woolhiser, AM.ASCE
Asst. Prof. of Civ. Engrg., Cornell Univ., Ithaca, N. Y.
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