Research On Numerical Modeling Of Smoothed Particle Hydrodynamics And Simulate Discharge Through Crest Orifice On Dam

There are many engineering problems, such as casting, crack propagation, explosion etc, which are not well suited to conventional computational methods, such as FEM, FVE, FDM. These methods are difficult to treat moving discontinuous problems. Viable strategy for these methods is to re-mesh in each step of the evolution. The mesh-free method is an approximation method based on nodes, and doesn't need a mesh entirely or partly. Then the discontinuous problems and the extremely large deformation problems can be solved without the re-meshing technique. Mesh-free method has been gained significant attention in the computational mechanics community. The author will research the mathematical model of Smoothed Particle Hydrodynamics (SPH) in this paper.The paper systematically introduces knowledge about theoretic basis and discretization method of SPH. Based on the interpolation theory, the author derives equations of the mathematical model of SPH, and derives equations on basis of that, which are equations of fluid dynamics.The equations of SPH have many formats, which can meet the mass conservation equation, momentum conservation equation and energy conservation equation, In this paper some related problems of SPH is discussed, such as kernel functions, smoothing length, boundary treatments and so on.The author makes two-dimensional program of SPH, and simulates free going out for small orifices in fluid mechanics and collapse of dam. Though the result calculated, the feasibility of this method and the program is proved.The author first applies the SPH model to the flow of liquid with free surface on Laxiwa dam, and simulates the process of the discharge of the surface outlet. The water recharge boundary is used in the model. The paper gives an analysis between numerical pressure and experimental pressure.