Research Article
Jan 1970
Numerical Solution of Saint-Venant Equations
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VIEW THE REPLYPublication: Journal of the Hydraulics Division
Volume 96, Issue 1
Abstract
The general, one-dimensional Saint-Venant equations are presented for a rigid open channel of arbitrary form, not necessarily prismatic, containing a flow that may be spatially varied. The theoretical basis for the method of characteristics is reviewed and used to show that, in the general case, the speed of long-wave disturbances is given by the slope of the characteristic curves. Finite-difference schemes on a rectangular net in the x - t plane and based on the characteristic forms of the Saint-Venant equations, as well as on the direct forms, are given and examined for their stability. The von Neumann technique for stability analysis is presented in detail. Explicit numerical schemes, which are simple, but require small steps in time because of stability problems, are contrasted with implicit schemes that permit numerical solution over large time steps but require the solution of large sets of simultaneous algebraic equations at each step. The double-sweep or progonka method, an exact time- and space-saving technique for solving these (locally linearized) equations, is also given in detail.
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Published In
Journal of the Hydraulics Division
Volume 96 • Issue 1 • January 1970
Pages: 223 - 252
Copyright
© 1970 American Society of Civil Engineers.
History
Published in print: Jan 1970
Published online: Feb 3, 2021
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Authors
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Theodor Strelkoff, AM.ASCE
Assoc. Prof. of Water Sci. and Civ. Engrg., Univ. of California at Davis, Davis, C. A
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