Numerical modeling of dam-break problems 1-D on dry bed
H. TORBI, F. BOUSHABA, A. YACHOUTTI, N. SALHI
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 on dray bed. 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 tow-step scheme, which is second-order in space and time. The performance and efficiency of the tow algorithms are illustrated and compared through dam break problems.
Keywords
References
[1] Alcrudo, . and Garcia Navarro, P. [1993] “A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations,” International Journal for Numerical Methods in Fluids 16(3), 489-505.
[2] Boulerhcha, Y. Secretan, G. Dhatt, D. N. Nguyen, G. M .[1995] “Application de la méthode des éléments finis aux équations 2-D hyperboliques : Partie I : équations scalaires d convection, ” Revue européenne des élments finis 4, 441-465.
[3] Vazquez-Cendan, M. E. [1999] “Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geomtry,” Journal of Computational Physics 148(2), 497-526.
[4] Zhou, J. G., Causon, D. M., Mingham, C. G. and Ingram, D. M. [[2001] “The surace gradient method for the treatment of source terms in the shallow-water equations,” Journal of Computational Physics 168(1), 1-25.
[5] Benkhaldoun, F., Elmahi, I. and Sead, M. [2010] “A new finite volume mthod for flux-gradient and source-term balancing in shallow water equations,” Comuter Methods in Applied Mechanics and Engineering 199(49), 3324-3335.
[6] Roe, P.L. [1981] “Approximate Riemann solvers, parameter vectors and differencs schemes,” Journal of Computational Physics 43, 357-372.
[7] Sead, M.[2004] “Non oscillatory relaxation methods for the shallow water equations in one and two space dimensions,” International Journal for Numerical Methods in Fluids 46(5), 457-484.
[8] Benkhaldoun, F., Elmahi, I. and Sead, M. [2007] “Well-balancd finite volume schemes for pollutant transport by shallow water equations on unstructured meshes,” Journal of computational physics 226(1), 180-203.
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