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

Hamid Reza Vosoughifar,Azam Dolatshah,Seyed Kazem Sadat Shokouhi

doi:10.1155/2013/642485

Abstract

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.

Highlights

Floods induced by dam failures can cause significant loss of human life and property damages, especially when located in highly populated regions
Erpicum et al presented a 2D finite volume (FV) multiblock flow solver, which was able to deal with the natural topography variation [20]
Baghlani utilized a combination of the robust and effective flux-difference splitting (FDS) and flux-vector splitting (FVS) methods to simulate dam break problems based on finite volume method (FVM) on a Cartesian grid

Summary

Introduction

Floods induced by dam failures can cause significant loss of human life and property damages, especially when located in highly populated regions. The shallow water equations (SWEs) are conventionally used to describe the unsteady open channel flow such as dam break. These equations are named as Saint Venant equations for one-dimensional (1D) problem and include the continuity and momentum equations for twodimensional (2D) studies. Singh et al developed a 2D numerical model to solve the SWEs for the simulation of dam break problems [23]. Shakibaeinia and Jin developed a new mesh-free particle model based on the weakly compressible MPS (WC-MPS) formulation for modeling the dam break problem over a mobile bed [25]. The local Lax-Friedrichs (LLxF) scheme is used for the estimation of fluxes at cells and the numerical approximation of hyperbolic conservation laws

Research Methodology

Discretization of Governing Equations

Results

Conclusions