American Society of Civil Engineers

Numerical Solution of Saint-Venant Equations

by Theodor Strelkoff, A.M.ASCE, (Assoc. Prof. of Water Sci. and Civ. Engrg., Univ. of California at Davis, Davis, CA)

Journal of the Hydraulics Division
, Vol. 96, No. 1, January 1970, pp. 223-252

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Document type: Journal Paper
Discussion: by Robert Shubinski    (See full record)
Closure:(See full record)
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.

ASCE Subject Headings:
Gradually varied flow
Mathematical models
Numerical analysis
Open channel flow
Unsteady flow
Water waves