Two-Dimensional Flow Model for Trapezoidal High-Velocity Channels

Abstract

A two-dimensional numerical flow model for trapezoidal high-velocity channels is developed. The model is designed specifically for simulation of flow in channels having sloping sidewalls in which the depth is an unknown variable in the governing equations and therefore the plan view of the flow domain is not known a priori. Solutions are obtained by time stepping from specified initial conditions using an implicit Petrov-Galerkin moving finite-element representation of the governing equations. The moving finite-element model produces a simultaneous solution for the boundary displacement and flow variables. This implementation provides stable solutions for supercritical flow even at relatively large Courant numbers. The model is tested by comparison of simulation results with laboratory data. These data sets serve as a basis for evaluation of the numerical model and should also prove useful to researchers in testing other numerical flow models applied to supercritical flow in channels having sloping sidewalls.