Investigations Of Smoothed Particle Hydrodynamics And Its Applications To Free Surface Flow Problems

Free surface flows in hydrodynamics widely exist in real life and engineering applications, and are associated with strong nonlinear physics. The free surfaces change with the flow and can lead to splashing, spreading, breaking and adhesion. How to efficiently and accurately model free surface flows in hydrodynamics is of theoretical and practical significance. Smoothed Particle Hydrodynamics (SPH), a Lagrangian, meshfree and particle method, has been developed rapidly and has already been applied successfully in bio-and nano-engineering, environmental engineering, national defense science and technology and so on. It has great advantages in dealing with problems with large deformation, deformable boundary, free surfaces, movement interfaces, and so on. SPH has special advantages over conventional grid-based numerical methods in dealing with complex grid, adaptive grid and multi-scale problems.This paper presented a comprehensive description of the basic equations and principles of SPH and its realization on the Navier-Stokes equation. In numerical aspects, this paper discusses re-initialization approach to improve density estimation, laminar viscosity and sub-particle-scale (SPS) model, artificial viscosity, manual compression, boundary treatment, variable smoothing length and nearest neighbor particle search method, etc. A surface tension model is also added into the SPH program.This paper focuses on the application of SPH in free surface flows in hydrodynamic. including the dam breaking problem and droplet splashing. Different numerical schemes are, comparatively studied with some revealing results. Four scenarios were modeled which include 1) dam breaking with solid obstacles,2) dam breaking without solid obstacles,3) droplet splashing on a solid wall, and 4) droplet splashing onto bulk liquid. The differences of the numerical results due to different modification terms are analyzed. For the dam breaking problem, it is shown that each simulation setup adopted in this paper can well capture the flow physics in dam breaking, especially in the interaction between water flow and rigid wall, such as splash, fusion, water rebound, variation of free surface, and severe deformation of flow pressure field near the wall. For the dam breaking prolem, the paper provided comparative analyses of the SPH numerical results with experimental observations, and numerical results obtained by using Moving Particle Semi-implicit (MPS) model and Volume of Fluid (VOF) model. While for the liquid splashing prolem, the paper also provided comparative analyses of the SPH numerical results with experimental observations, and numerical results obtained by using Least Square Finite Element Method (LSFEM) model. Finally it is concluded that the numerical simulations of dam breaking problem and liquid splashing problem have demonstrated the effectiveness and reliability of the improved SPH numerical schemes and the SPH code.