Depth-Averaged Open-Channel Flow Model

Abstract

A general mathematical model is developed to solve unsteady, depth-averaged equations. The model uses boundary-fitted coordinates, includes effective stresses, and may be used to analyze sub- and supercritical flows. The time differencing is accomplished using a second-order accurate Beam and Warming approximation, while the spatial derivatives are approximated by second-order accurate central differencing. The equations are solved on a nonstaggered grid using an alternating-direction-implicit scheme. To enhance applicability, the equations are solved in transformed computational coordinates. The effective stresses are modeled by incorporating a constant eddy-viscosity turbulence model to approximate the turbulent Reynolds stresses. As is customary, the stresses due to depth-averaging are neglected. Excluding recirculating flows, it is observed that in most cases the effective stresses do not significantly affect the converged solution. The model is used to analyze a wide variety of hydraulics problems including flow in a channel with a hydraulic jump, flow in a channel contraction, flow near a spur-dike, flow in a 180° channel bend, and a dam-break simulation. For each of these cases, the computed results are compared with experimental data. The agreement between the computed and experimental results is satisfactory.