Collocated Discrete Least Squares Meshless (CDLSM) Method for Simulation of Mobile- Bed Dam Break Problems

Meshless methods have been added to numerical methods in recent decades, and have provided a wide range of scientific, research and engineering fields. The use of Meshless methods is still not extent to the finite element methods in engineering issues, but these methods may now be similar to those of the time when the finite element method begins to expand. In this research, a discrete least square meshless method with collocation points CDLSM is proposed. The concepts, mathematical relations, and formulation of this method are fully presented. In this simulation, collocation points are used for more efficiency and lower computing time by using least squares method, as well as using the series instead of integrals (discrete mode). Based on this method, the dam failure phenomenon has been solved in different cases and its verification has been used by comparison with analytical solution with experimental data whenever it is available. Comparison of numerical results with existing analytical and experimental data shows that the method has high efficiency and simulates the shock or discontinuity.