Modeling of dam Break Using the Meshless Local Petrov-Galerkin Method and Shallow Water Equations

Dam break is one of the most important problem of water engineering. many researchers have studied this phenomenon.  The equations governing for dam break are shallow water equations.  Many researchers have tried to investigate the dam breaking phenomenon using numerical methods. Most of these numerical methods, such as finite volume method, are being used to solve differential equation in some simple and complex case with meshing problem domain. Recently new numerical methods called Meshless methods have been developed to solve differential equations. these methods need no meshing or re-meshing on the domain the shortages of meshing disappeared. In this research, shallow water equations were modeled using a Meshless Local Petro-Gallerkin method (MLPG) with Moving Least Squares (MLS) shape function.  Then, using a standard example, the model's accuracy was investigating and the model error rate was calculated.  it was indicated that the model has a good accuracy, so that the root mean square error was 0.00246 respectively.  Finally, using the model, the dam break problem was simulated and the results were compared with the solutions of the Galerkin-free method.