Research On Algorithm Of Smoothed Particle Hydrodynamics

With the development of hardware and software for computer, numerical simulation has increasingly become a very important approach for solving complex practical problems. Comparing with traditional experiments, numerical simulation doesn't carry out expensive, time-consuming or even dangerous experiments, and according to the demand of research, it can get complete and insightful information, which may be impossible to obtain during traditional experiments. At present, there are two numerical calculation methods: mesh method and meshfree method. General mesh method, such as FDM and FEM, has been used in various fields of computational fluid mechanics and computational solid mechanics, no matter how widely these methods can be used, there are still so many difficulties with large deformed and numerical incontinuous problems, and meshfree method is very suitable for such problems.Based on predicting the impact wave loads on shipside and ship-deck, this study introduces a meshfree method-Smoothed Particle Hydrodynamics technique among various calculation methods. The basic theory of SPH is interpolation algorithm. This method translates the continuous fluid conservation equations, which are in the form of partial differential representation, into the form of integration description by means of kernel approximation, and transforms the continuous form of control equations into discrete form by particle approximation method. SPH method is applied to the area of astronomic physics at first, it is a new approach in the field of hydrodynamics and at the stage of theoretical research at present.This paper is focused on the further investigation on the basic theory of SPH approach, and prepares for wide application in the fields of shipbuilding and ocean engineering. For this reason, the following problems are emphatically investigated.Firstly, this paper introduces the basic conception of SPH method, especially describes the history of SPH method, the development of SPH method and the actuality of SPH method. Furthermore, this study introduces the advantage and disadvantage of SPH method, and the range of application for SPH method.Secondly, the step of getting basic formulation of SPH method is represented, and the idea of calculation is introduced. The kernel function approximation and particle approximation are further investigated. This study introduces some kinds of kernel function, and represents the procedure of function construction.Thirdly, the approximation approach of fluid dynamic equations in SPH form is presented. This paper gives Navier-Stockes equations in Lagrange form, and presents different forms of continuous equation, momentum equation and energy equation.At last, we simulate some typical fluid problems, for instance, Poiseuille flow and Couette flow. On the one hand the precision of the algorithm can be validated, and on the other hand the regular of the algorithm can be mastered. Furthermore, this study attempts to simulate other typical fluid problems, such as flow pass a cylinder and dam collapse, and evaluates the extension of application for SPH method.