Depth-Averaged Simulation of Supercritical Flow in Channel with Wavy Sidewall

Abstract

Supercritical flow in a channel with a wavy sidewall is numerically simulated by solving the two-dimensional (2D) depth-averaged equations using two different second-order accurate finite-difference schemes: ADI and MAC. ADI is an implicit model that uses an alternating-direction-implicit (ADI) scheme to solve the governing equations. MAC is an explicit model employing the MacCormack two-step predictor-corrector scheme. To accurately simulate the wavy sidewall, both models solve the governing equations in transformed computational coordinates. Bottom friction is computed using the Manning formula and the effective stresses are modeled with a constant eddy-viscosity turbulence model. As is customary, the stresses due to depth-averaging are neglected. The computed water depth in the channel is compared with experimental data obtained by Mizumura. The effect of bottom friction, effective stresses, artificial viscosity, grid geometry, boundary conditions, and the Courant-Friedrichs-Lewy (CFL) number are investigated. Similarities and differences in the behavior of the models are observed and discussed.