Journal of Applied Mathematics
Volume 2013 (2013), Article ID 642485, 12 pages
Research Article

Discretization of Multidimensional Mathematical Equations of Dam Break Phenomena Using a Novel Approach of Finite Volume Method

1Department of Civil Engineering, Islamic Azad University, South Tehran Branch, 17776 Tehran, Iran
2Department of Civil Engineering, Islamic Azad University, Dezful Branch, Khuzestan, 313 Dezful, Iran

Received 11 July 2012; Accepted 2 February 2013

Academic Editor: Chein-Shan Liu

Copyright © 2013 Hamid Reza Vosoughifar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper was concerned to simulate both wet and dry bed dam break problems. A high-resolution finite volume method (FVM) was employed to solve the one-dimensional (1D) and two-dimensional (2D) shallow water equations (SWEs) using an unstructured Voronoi mesh grid. In this attempt, the robust local Lax-Friedrichs (LLxF) scheme was used for the calculating of the numerical flux at cells interfaces. The model named V-Break was run under the asymmetry partial and circular dam break conditions and then verified by comparing the model outputs with the documented results. Due to a precise agreement between those output and documented results, the V-Break could be considered as a reliable method for dealing with shallow water (SW) and shock problems, especially those having discontinuities. In addition, statistical observations indicated a good conformity between the V-Break and analytical results clearly.