Title: Numerical simulation of flood due to dam-break flow using an implicit method

Authors: Majid Galoie; Gerald Zenz; Saeid Eslamian; Artemis Motamedi

Addresses: Institute of Hydraulic Engineering and Water Resources Management, Graz University of Technology, Stremayrgasse 10/II, A-8010, Graz, Austria. ' Institute of Hydraulic Engineering and Water Resources Management, Graz University of Technology, Stremayrgasse 10/II, A-8010, Graz, Austria. ' Department of Water Engineering, Collage of Agriculture, Isfahan University of Technology, Isfahan 8415683111, Iran. ' Department of Water Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran; Institute of Hydraulic Engineering and Water Resources Management, Graz University of Technology (TUGraz-Austria), Stremayrgasse 10/II, A-8010, Graz, Austria

Abstract: In this paper, the depth-averaged 2D shallow water equations in the non-conservative form are solved based on the 'Beam and Warming' implicit method by means of the finite difference method (FDM) having a second-order accurate on time and first-order accurate on space. Variations in each time step are calculated considering equations in both x and y directions. Due to solving an equation system in any row, a special algorithm, so-called block-tridiagonal system of equations algorithm, is utilised. To solve the aforementioned dam break equations, a computer programme based on the numerical equations has been developed. Finally, this programme has been validated against the analytical and numerical solutions of some problems obtained from the literature and comparison between this method and other solutions shows a good agreement.

Keywords: dam break flow; shallow water equations; Beam and Warming implicit method; block-tridiagonal system of equations; Seiche test; floods; flooding; finite difference method; FDM.

DOI: 10.1504/IJHST.2012.047429

International Journal of Hydrology Science and Technology, 2012 Vol.2 No.2, pp.117 - 137

Available online: 19 Jun 2012 *

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