NUMERICAL SIMULATION OF TWO-DIMENSIONAL SUPERCRITICAL FLOWS USING A PREDICTOR-CORRECTOR FINITE DIFFERENCES SCHEME

F. MERAH, A. BERREKSI, T. IKNI, S. BENMAMAR, S. HAMCHAOUI, A. BENZERRA, A. BEDJOU

Abstract


The phenomenon treated in the present research work relates to unsteady two-dimensional free-surface flows in a torrential regime. These flows are governed by Saint-Venant equations which are obtained from the depth integration of the three-dimensional Navier-Stokes equations, taking into account some assumptions in order to simplify the mathematical model governing the type of flow studied. The determined equations cannot be solved theoretically by known algebraic methods. Several numerical methods have been developed to date to solve partial differential equations. In the present study, we opt for the finite difference method. The discretization of the governing equations is done using a Gabutti Predictor-Corrector scheme. A numerical model is developed in order to determine the flow network in a symmetrical transition zone of a free surface channel. It is recalled that this type of structure is widely used in hydraulics, mainly in spillways chutes. These transitions can be either expansions or contractions. In this case, we propose to analyse the flow of water through a hydraulic structure composed of a gradual expansion. The knowledge of the wave system is very important in order to properly dimension this kind of hydraulic structures. The aim is to calculate the water line along the median axis and the sidewall, then move on to a parametric study in which the influence of varying the Manning's roughness number and the upstream width of the channel expansion on the shape of the water line will be analysed.


Keywords


2D unsteady flow, Torrential regime, Saint-Venant, Shock wave, finite differences

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References


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