The application of implicit method to open-channel surges

Abstract

The implicit method of flood routing has been modified so as to make it applicable to open-channel shocks.

The output of the computer program with θ = 0.6 compared favorably with the experimental result. A comparison was also made with other explicit schemes and a two step implicit scheme proposed by other investigators. The implicit method with θ = 0.6 gave results as good as the explicit scheme and much better than the two step implicit scheme.

In this method the equations of continuity and momentum for gradually varied flow have been written in finite difference form for a point in the (x,t) plane specified by the co-ordinates (x+dx/2, t+θdt). The variable e was made to take on values from 0 to 1.0. A computer program was written to obtain the output hydrograph at the downstream end of a rectangular channel for any type of inflow hydrograph at the upstream end of the channel. Three types of inflow hydrographs were chosen and the outflow hydrographs were obtained for different values of θ. For that type of inflow hydrograph that caused a surge to occur in the channel, it was found that θ = 0.6 gave the most satisfactory results.

Experimental results of a surge in a channel were obtained from published literature.