On the accuracy of one-dimensional models of steady converging/diverging open channel flows

Abstract

Shallow water flows through open channels with varying breadth are commonly modelled by a system of one-dimensional equations, despite the two-dimensional nature of the geometry and the solution. In this work steady state flows in converging/diverging channels are studied in order to determine the range of parameters (flow speed and channel breadth) for which the assumption of quasi-one-dimensional flow is valid. This is done by comparing both exact and numerical solutions of the one-dimensional model with numerical solutions of the corresponding two-dimensional flows. It is shown that even for apparently gentle constrictions, for which the assumptions from which the one-dimensional model is derived are valid, significant differences can occur. Furthermore, it is shown how the nature of the flow depends on the manner in which the boundary conditions are applied by contrasting the solutions, obtained from two commonly used approaches. A brief description is also given of the numerical methods, developed recently for the solution of the one- and two-dimensional shallow water equations, and used to produce the results presented in this paper. Copyright © 2001 John Wiley & Sons, Ltd.