One and Two Dimensional Dam Break Flow Modeling by an Implicit Method(Gradually Dam Failure Included)

The dam break flow is a hydraulic phenomenon which is a kind of rapidly varied unsteady flow. The shallow water equations, considered as the basic and governing equations, are the depth average of Navier-Stocks equations in which the vertical component of speed vector is neglected and the horizontal one is considered as thedepth average of equations. In this paper, the shallow water equations are solved based on the Beam and Warming implicit method by means of the Finite DifferenceMethod (FDM) having a Second-Order accurate on time and First-Order accurate onspace. Variations in each time step are calculated considering equations in both x andy directions. Due to solving an equation system in any row, a special algorithm, socalled Block-Tridiagonal system of equations algorithm, is utilized. To solve the aforementioned dam break equations, a computer program based on the numericalequations has been developed. Finally, this program has been validated against the analytical and numericalsolutions of some problems obtained from the literature and comparison between this method and other solutions shows good agreement.

کلیدواژه ها:

shallow water equations ، the Beam and Warming implicit method ، Dam break flow ، Block-Tridiagonal system of equations ، rapidly varied unsteady flow