Appllication Of The Finite Point Meshless Method In Simulation Of Steady Groundwater Flow

The meshless method is a new type of numerical algorithm and developing in recent yea- rs.As its trial function does not rely on the grid,this method in the solution of the research fiel- d with large deformation and moving boundary shows its advantages.The differences between various types of meshless methods depend on different trial functions and discrete programs. The finite point method in this article uses the moving least square approximation function as a trial function and collocation method as its discrete program.The basic principle of moving least square approximation is to structure local approximation for each node. The values of all local approximation functions in every node constitute the global approximation function.So calculations using moving least square approximation have high accuracy. Collocation meshl- ess method is a pure meshfree method, comparing with Galerkin method which is another commonly-used discrete program, the finite point method does not require any grid integral,so it is easy to be implemented and has higher efficiency.This article discusses the basic principle of the finite point method and its error estimates. Then it is applied to the numerical simulation of groundwater flow.This paper is divided into five parts.In the first chapter,the background,history and development of the meshless method are introduced,and major research in this paper is pointed out. In the second chapter ,the basic principle of the meshless method is elaborated. In the third chapter, the basic principle of the finite point method is described in great detail using steady groundwater flow model,and then error estimates for the finite point method which provide a theoretical basis for its implemen- tation are discussed. In the fourth chapter, Application of the finite point method for solving two-dimensional heterogeneous porous media of steady groundwater flow in three kinds of parameters is finished. The results show that the finite point method used to solve the problem of such a model of groundwater is very effective. In the fifth chapter,the whole paper is suma- rized and further research focus is pointed out.