Finite volume and finite element method

for the simulation of one dimensional dam break problems in dry regions

 

A. Yachouti1*, F. Boushaba1, M. Boulerhcha2

1 Université Mohammed Premier, Ecole Nationale des Sciences Appliquées, Oujda

2 Université Mohammed Premier, Faculté des Sciences, Oujda.

* Corresponding author. E-mail: yachoutti@gmail.com

Received: 07 March 2013; revised version accepted: 02 January 2014

 


Abstract

     This paper is concerned with the application and comparison of a finite element Taylor Galerkin and finite volume method for the simulation of shallow water flows to model dam break problems. The finite volume scheme uses Roe’s approximate Riemann solver to evaluate the convection terms combined with the MUSCL technique to achieve second-order accuracy in space. The finite element model is based on the Lax–Wendroff two-step scheme, which is second-order in space and time. The performance and efficiency of the two algorithms are illustrated and compared through dam break problems over wet and dry beds.

 

Keywords: Shallow-water equations; Finite element; Lax-Wendroff scheme; Finite volume; Roe’s scheme; MUSCL technique; Dry area.

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