Mathematical simulation of one-dimensional dam-collapse flow over wetted bed

¹ Mechanics Institute of Ben Mhidi University, PO Box 358, Oum-El-Bouaghi, 04000, Algeria
² Mechanics department of Mentouri University, Constantine, 25000, Algeria

Corresponding author: d-medkour@caramail.com

Received: 17 May 2002
Accepted: 9 January 2003
Published online: 10 April 2003

Abstract

A mathematical model is described and applied to simulate sudden total one-dimensional dam-break flow over wetted bed. The dam collapse takes place in a rough sloping non-prismatic channel of various cross-sections. The water parameters to be instantaneously calculated are the height h, the discharge Q, the mean velocity u and the pressure force P. The mentioned flow is governed by the Saint-Venant shallow water equations and the computation process, on the basis of rectangular grid of points, consists of two complementary solutions: (a) at the first instant after the collapse, an analytical procedure is considered. The calculated parameters are taken as initial values in the water stream embraced by the flood wave. Outside this zone, initial conditions are those which preexist before the rupture. (b) Beyond this time, a numerical computation is carried out by using an iterative explicit method of characteristics. (c) Every time stage of calculation starts by determining the discontinuity (wave front) parameters namely its abscissa x_δ, height h_δ, celerity c_δ and alert delay t_δ. The former is the discontinuity arrival time at considered station. Typical results are obtained and compared with similar ones already published by others in the literature.