Characteristic Based Split Finite Element for Unsteady DamBreak Problem

In this paper, an efficient numerical model for solution of the twodimensional unsteady dambreak problem is described. The model solves the shallow water equations through CharacteristicBased Split (CBS) finite element method. The formulation of the model is based upon the fractional time step technique primarily used in the finite difference method for the incompressible NavierStokes equations. In addition to wellknown advantages of the finite element discretization in introducing complex geometries and making accurate results near the boundaries, the CBS utilizes interesting advantages. These include the ability of the method to simulate both compressible and incompressible flows using the same formulation. Improved stability of the CBS algorithm along with its capability to simulate both sub and supercritical flows are other main advantages of the method. These useful advantages of the algorithm introduce the CBS as a unique procedure to solve fluid dynamics problems under various conditions. Since dambreak problem has principally a high nonlinear nature, the model is verified firstly by modeling onedimensional problems of dambreak and bore formation problems. Furthermore, application of the model to a twodimensional hypothetical dambreak problem shows the robustness and efficiency of the procedure. Despite the high nonlinearity nature of the solved problems, the computational results, compared with the analytical solutions and reported results of other numerical models, indicate the favorable performance of the used procedure in modeling the dambreak problems.