A Multimode Scheme of Characteristic Method for Open Channel Flows

by Wenchin Lin, Univ of Minnesota, Minneapolis, United States,
Charles C. S. Song, Univ of Minnesota, Minneapolis, United States,



Document Type: Proceeding Paper

Part of: Hydraulic Engineering

Abstract:

This paper deals with the stability and accuracy of a multimode scheme, based on the method of characteristics, for unsteady one-dimensional open-channels flows. This scheme combines three known computational schemes (classical, spatial reachout, and boundary implicit schemes) in such a way that the choice of time step size is free from the CFL stability constraint. The accuracy of the scheme has been studied numerically for simple harmonic waves traveling in a channel of circular cross section. The calculated attenuation and dispersion of the traveling waves in a horizontal channel under zero friction conditions are used as the measure of the accuracy of the scheme. Two sources of numerical errors, (1) that due to inadequate resolution of special and temporal variations of the flow and (2) that due to the accumulation of truncation and round off errors, have been recognized. As expected, the first type of errors decreases as the relative grid sizes ▵?/L and ▵t/T are decreased. The second type of the errors is found to be a function of the Courant number, C_r, with the minium occurring at C_r=1. For a fixed ▵?, the numerical error increases when ▵t is either increased or decreased from its critical value.

Subject Headings: Numerical methods | Open channel flow | Water waves | Fluid flow | Wave propagation | Unsteady flow | One-dimensional flow

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