Title: Numerical study using an implicit finite difference scheme of a high velocity flow crossing a non-prismatic hydraulic structure – case of symmetrical gradual expansion

Authors: Ali Berreksi; Tahar Ikni; Saâdia Benmamar; Lyes Amara; Samir Hamchaoui; Abbas Benzerra; Boualem Remini

Addresses: Laboratoire de Recherche en Hydraulique Appliquée et Environnement (LRHAE), Département d'Hydraulique, Faculté de Technologie, Université de Bejaia, Route de Targa Ouzemmour, Bejaia, 06000, Algeria Fax: +213-34215105 ' Laboratoire de Recherche en Hydraulique Appliquée et Environnement (LRHAE), Département d'Hydraulique, Université de Bejaia, Route de Targa Ouzemmour, Bejaia, 06000, Algeria ' Research Laboratory of Water Sciences (LRS-Eau), Notional Polytechnic School of Algiers, Algeria ' LARHYSS Research Laboratory, University of Biskra, P.O. Box 145, R.P., 07000, Biskra, Algeria ' Laboratoire de Recherche en Hydraulique Appliquée et Environnement (LRHAE), Département d'Hydraulique, Université de Bejaia, Route de Targa Ouzemmour, Bejaia, 06000, Algeria ' Laboratoire de Recherche en Hydraulique Appliquée et Environnement (LRHAE), Département d'Hydraulique, Université de Bejaia, Route de Targa Ouzemmour, Bejaia, 06000, Algeria ' LARHYSS Research Laboratory, University of Biskra, P.O. Box 145, R.P., 07000, Biskra, Algeria

Abstract: The objective of the present research work is the numerical simulation of a supercritical flow through a non-prismatic channel. The unsteady flow is governed by the 2D Saint Venant equations. These equations are discretised using the Beam and Warming implicit finite difference scheme. The elaborated numerical model is tested in the case of a symmetrical gradual expansion. First, the aim is to determine the shape of the water surface along the solid wall and the median axis for a weak bottom slope. Subsequently, the study is generalised for steeply sloping channels. The obtained results in the first application show that there are no significant disturbances in the water surface, which did not lead to the appearance of the rather dangerous transverse waves. In the second one, it was observed that by increasing the bottom slope the flow does not extend laterally towards the walls because their divergence is very gradual.

Keywords: high velocity flow; 2D transient flow; implicit scheme; non-prismatic channel; variable bottom slope.

DOI: 10.1504/IJHST.2022.124544

International Journal of Hydrology Science and Technology, 2022 Vol.14 No.2, pp.109 - 123

Received: 21 Feb 2020
Accepted: 13 Oct 2020
Published online: 28 Jul 2022 *

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