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Abstract
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Background: Dam break is one of the events that have a lot of financial and life consequences. Therefore, this phenomenon should be thoroughly studied when designing dams in order to provide the necessary measures for controlling large flood damages caused by the dam. The problem of dam break has been long considered by the researchers due to the collision with the suddenly release of a large volume of water behind the dam and emergence of extreme waves with high speed with low time for warning. In order to investigate the break phenomenon, researchers have considered the equations which govern shallow waters and suggested different numerical methods due to the lack of precise mathematical methods for solving these equations in general.
Aim: The purpose of this research is to solve the shallow water equations for numerical simulation of dam breaking phenomenon with DQ method in two dimensions.
Methodology: One of the numerical methods that can be used to solve differential equations governing the dam breaking phenomenon is the Differential Quadrature (DQ) numerical method. The DQ method is a high-order numerical method, and unlike lower-order numerical methods such as FV, FD, FE, there are fewer network points to achieve accurate results. This method is used to solve partial differential equations for boundary value problems and initiation of a value. In the DQ method, a partial derivative of a function in a particular direction is interpolated by a set of values of functions weighed in the points of a discrete region in the same direction. In order to study the developed model, various basic issues including dam and water column breakdown by DQ method have been solved and discrete operations.
Results: After disjointing and coding of shallow water equations, the results were compared with non-trivial results that indicated the accuracy of the Quadrachver method in solving shallow water equations.
Conclusions: Comparing the results with the references proved the high
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