Numerical Solution for One-Dimensional Open-Channel Transient Flow

Abstract

In this paper, consideration is given to the numerical solution of the transient flow in prismatic open channels. The mathematical formulation is based on the application of mass and momentum conservation laws. This problem has been solved by two methods, which are: the characteristics grid method, using non-linear integration, and the finite difference conservative scheme. Two applications of transient flow in rectangular channel are considered. To verify the validity of the used numerical techniques, the computed results are compared for different boundary conditions. These comparisons demonstrate that results obtained by the method of characteristics agree with those of the conservative finite difference method when no hydraulic bore occurs. Nevertheless, the finite difference conservative method is more practical and can capture the hydraulic bore with precision and without any special treatment. A further comparison shows good agreement between finite difference method results and literature-quoted numerical computations.

Key Words:

• Open-channel flow
• transient flow
• characteristics method
• finite

Additional information

Notes on contributors

A. Triki

Ali Triki is a mechanical engineer and teaching assistant in fluid mechanics at the Department of Mechanical Engineering at the Engineering School of Sfax, Tunisia. He has a master’s degree in mechanics and engineering. His research interests include open-channel transient flow, dam break and fluid-structure interaction. He is a specialist in numerical methods simulating the partial differential equations of hyperbolic type.

E. Hadj-Taïeb

Ezzeddine E. Hadj-Taïeb is a professor of fluid mechanics in the Department of Mechanics at the National Engineering School of Sfax, Tunisia. He has a master’s degree and Ph.D. in fluid mechanics from Fluid Mechanics Institute and Polytechnic institute of Toulouse in France. He has more than 30 years of experience in the area of steady-state and transient modelling. He is a specialist in analyzing and simulating wave propagation in fluid and solid mediums. He has written more than 20 articles. His research interests include engineering hydraulics and modelling water supply networks, transient flow, transient two-phase flow and fluid-structure interaction.