Stable Numerical Model for Transcritical Flow and Sediment Transport on Uneven Bathymetry

Abstract

A stable and well-balanced finite volume method was proposed to solve the shallow water equations coupled with a sediment transport equation. An approximate Riemann solver with a monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction was used for the computation of the flux terms. A special but relatively simple treatment of source terms made it possible to ensure numerically and physically balanced computational results on very steep sloped beds. Various numerical simulations conducted on rigid beds have demonstrated that the proposed numerical scheme could provide stable computational results in the cases of flat and nonflat bottoms. From the comparisons of experiments on erodible beds in one- and two-dimensional channels, good agreement was obtained when proper parameters for turbulent flow and sediment transport were provided. Lastly, the effects of the parameters in relation to hydraulic characteristics included in the flow and the sediment transport models were investigated and briefly discussed.