Title: Numerical study of shallow-water equations using three explicit schemes - application to dam break flood wave

Authors: Tahar Ikni; Ali Berreksi; Mohamed Belhocine

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 ' 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 ' 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

Abstract: The numerical method to solve dam break problem on regular bathymetry was developed. Two cases of dam break wave propagation on wet and dry bottoms were selected to verify the numerical model elaborated. Three numerical schemes of Lax-Friedrichs, Adams-Bashforth and Adams-Bashforth-Adams-Moulton are applied to simulate this phenomenon using the 1D Saint-Venant equations. An artificial viscosity is added to these numerical schemes to provide stability and reduce numerical diffusion. This viscosity makes the numerical scheme robust (very powerful) for the simulation of this phenomenon. The results obtained show that these developed models are able to simulate dam break wave propagation process. The relative error in the L1 norm between the computed results and analytical solutions is calculated. The L1 norm indicates that the Adams-Bashforth-Adams-Moulton scheme has better accuracy than the other two schemes. It is shown that the technique used is simple, accurate, robust and stable for the simulation of the dam break wave propagation on wet and dry bed conditions.

Keywords: dam break; explicit schemes; artificial viscosity; Lax-Friedrichs; Adams-Bashforth; Adams-Moulton.

DOI: 10.1504/IJHST.2021.116662

International Journal of Hydrology Science and Technology, 2021 Vol.12 No.2, pp.101 - 115

Received: 27 Feb 2020
Accepted: 24 Apr 2020

Published online: 01 Jul 2021 *

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