The Application Of SPH And MPS In Simulating Viscous Free-Surface Flows

SPH (Smoothed Particle Hydrodynamics) and MPS (Moving Particle Semi Implicit) as mesh-free, Lagrange particle method, are recently developed. It has been widely applied in Computational Fluid Dynamics and other relative subjects. Compared with other grid-based numerical methods, the most advantage of SPH and MPS is that it can naturally handle hydrodynamic problems with extremely large deformation of the free surface. In this thesis, the application of SPH and MPS method in Simulating Viscous Free-Surface Flows is investigated, this subject is not only significant in theory, but also has good prospect of engineering application.SPH and MPS have excellent flexibility in dealing with large-deformed free surface flows. But there are some differences between SPH and MPS on numerical scheme, computational efficiency, and speed of convergence. A 2-D dam breaking problem is chosen to be simulated by the SPH and MPS to investigate these two methods, the numerical results show that the profile of water by the SPH is usually clearer and smoother, while those obtained by the MPS present a splashing and violent free surface. In addition, convergence is investigated, the results show that suitable large particle number is essential to capture the details of flow, and the convergence rate of the MPS is quicker than that of the SPH as the initial space distance between neighboring particles decreasing. The adopted time step doesn't make too much effect on the results when the CFL condition is satisfied. For computational efficiency, the SPH is more efficient in dealing with large-scale free surface flows while the MPS method is very time-consuming to solve linear system equations. Through the investigation, we provide a basis for selection of different mesh-free particle methods for specific problem.Base on the investigation, MPS is extended to hydraulic jump problems in 2-D and 3-D. Hydraulic Jump is a fascinating hydraulic phenomenon, and we use MPS method to simulate the hydraulic jump's generation together with its traverse. Numerical results show that MPS have excellent flexibility and reliability in dealing with complicated free surface flows, their numerical simulation can predict the shape and position of free surface very well. Different types of hydraulic jump's behavior are investigated. It is observed that there is a splash of water surge up the wall and the front of bore becomes a breaker wave when Hydraulic Jump has a high speed while a so-called "undular bore" is formed when the speed is lower. When the Hydraulic Jump interacting with a Square column, the free surface becomes less violent.As highly non-linear physical processes, the wave breaking and post-breaking are of crucial engineering importance. A new kernel function of MPS is proposed for accurate tracking of water surface in breaking and post-breaking of solitary wave. A numerical tank has been build based on MPS method to simulate the breaking and post-breaking of solitary wave on a plane slope; the run-un of solitary wave on a vertical wall; the interaction between solitary wave and plate.