Unsteady flow regulation in open channel by using inverse explicit method

Abstract

Flood routing and operation-type problems are two major problems which are required to be solved frequently in unsteady flow problems in open channels. Now-a-days for routing and regulating problem, generally the Saint-Venant equation is used to predict the discharge and water stage at the study area in the channel. Routing of flood calculates the discharge and flow depth at future time series. On the other hand the operation problem is mainly used to compute the inflow at required upstream section for regulating structure of the delivery system to get a predefined water demand at required section at downstream end of the channel. So it is the inverse computational problem from downstream to the study section at upstream. So an explicit finite difference scheme which is solved from downstream to upstream also known as inverse explicit scheme is presented to solve the operation type problem in open channels. The finite difference inverse explicit scheme is applied to solve the Saint-Venant equations based on the discretization of the Preissmann implicit scheme. In this research the finite difference inverse explicit method is applied to a rectangular canal. The computation is performed by proceeding first backward in time and then backward in space from downstream. The method is numerically stable and the computed upstream discharge hydrograph by the inverse explicit scheme, when used as upstream boundary condition in the routing problem by the HEC-RAS commercial computer model, reproduce downstream flow hydrographs very close to the predefined outflow. The suitable value of weighting coefficient in terms of time (∅) and time step (∆t) is determined.