Theoretical Research And Application On The Numerical Method Of Free Surface Flow

The numerical simulation of free surface flow has been a hot and difficult problem in the field of hydrodynamics and computational fluid dynamics research. The numerical simulation of the free surface flow involved almost all the theory of computational fluid dynamics methods and cutting-edge technology. the question of Free surface flow has been existed in the engineering field, such as ship hydrodynamics, aerospace, hydraulic engineering, mechanical engineering, petrochemical engineering and civil engineering, and so on., Therefore, the problem of free surface flow numerical method of research was important and significance both in theory and in practical engineering.Firstly, the popular numerical methods of the free surface flows were reviewed and investigated systematically. The VOF (Volume of Fluid) method for the interface reconstruction based on the Euler grid, which was containd by Hirt and Nichols method, FLAIR method, Youngs method, FCT method, and Level Set Method based on unstructured grid FVM (Finite Volume Method), and SPH(Smoothed Partical Hydrodynamics) based on the meshfree method, all of which, the basic theory were elaborated in detail.The numerical methods aboved were compared and analyzed by simulating the three classic examples, which were simple convection flow field, a rotational flow field, and a shear flow field.And selected a finer method from aboved methods by the effect of free surface tracking, and the finer mthod was SPH, which would be discussed in this paper.SPH control equations which can be applied to generalized hydrokinetics and related numerical techniques were studied. SPH control equations were derived from Lagrangian equations. Viscosity problem was simulated and solved by applying SPH expression which contained viscosity. Incompressible fluid was converted to approximated incompressible fluid to be solved and analyzed by using artificial compressibility and selecting corresponding state equation. The solution of the solid wall boundary conditions and free boundary conditions, time integration method and time step identification, especially the method for searching free surface particles, all of which were discussed.Based on the condition about Riemann condition and SPH method of the generalized hydrokinetics, a new method of how to search the free surface particles and how to calculate free surface tension was determined. SPH numerical simulation was enforced by a Fortran program to simulate the problem of a drop impacting free liquid surface, and its results were compared with the level set result.SPH method was applied to simulate free surface flow in the practical engineering field. And the two numerical simulation was finished by SPH, which are the liquid sloshing in ship hydrodynamics field and the discharge through crest orifice on dam in the hydraulic engineering field.