Title: Improvements of the Vasiliev's box-scheme for transcritical flows in open channel
Author: Maurizio Venutelli
Address: Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, 1, I-56126 Pisa, Italy
Abstract: Vasiliev's fully implicit finite difference box scheme, used in hydraulic engineering to simulate flood routing and overland flow, is invalid, in its usual implementation, for modelling transcritical flow. Short waves, generated near regions of steep gradients, and responsible for the often observed grid-to-grid oscillations, are not damped. In order, to suppress these spurious oscillations, which degrade and successively instabilise the solution, the adaptive smoothing approach is applied herein. The remedy confines the damping only near sharp gradients, and unaffects the regions where the flow is relatively smooth. In addition, weighted in time the spatial derivative approximations, the prevention of the dissipation in a broad spectrum of wave number, is obtained. By Fourier linear analysis, the stability, the convergence, and the variations of the time-weighted parameter, of the Courant number, of the Froude number, of the frictional parameter, and of the viscosity coefficient are investigated. Benchmark test cases, involving transcritical flow, friction, non-uniform bed slopes, and non-prismatic channels, and laboratory dam-break simulations, compared to the analytical solutions, and the experimental data, are presented.
Keywords: finite difference box scheme; shallow water equations; Fourier analysis; open channels; transcritical flow; Vasiliev; hydraulic engineering; flood routing; overland flow; modelling; short waves; grid-to-grid oscillations; adaptive smoothing; damping; Courant number; Froude number; viscosity coefficient; friction; non-uniform bed slopes; non-prismatic channels; dam break simulation.
Progress in Computational Fluid Dynamics, An Int. J., 2013 Vol.13, No.6, pp.382 - 396
Available online: 08 Oct 2013