In this paper, a numerical solver is developed for the computation of one and two dimensional dam break problems. The considered equations are the 2D shallow water equations written in conservative form. The algorithm uses a finite volume method which is based on Roe's approximate Riemann solver. It is of second order in space and time, and can be used on complicated geometries with unstructured meshes. The stiffness coming from discontinuity propagation due to the dam is taken into account by the introduction of a dynamical mesh refinement-unrefinement procedure. The results presented on some benchmark dam break situations including wet/dry beds, and comparisons with analytical solutions, show the accuracy of the used methods and the efficiency of the adaptation technique in the simulation of such phenomena.

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This paper presents numerical solvers, based on the finite volume method. This scheme solves dam break problems on the dry bottom in 2D configuration. The difficulty of the simulation of this type of problem lies in the propagation of shocks on the dry bottom. The equation model used is the shallow water equations written in conservative form. The scheme used is second order in space and time. The method is modified to treat dry bottoms. The validity of the method is demonstrated over the dam break example. A comparison with finite elements shows the weakness and robustness of each method.

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