Solving The Problem Of Groundwater Flow Using Radial Basis Function Partition Of Unity Collocation Method

In recent year, meshless method for solving partial differential equation has great development, an increasing number of people have began to research meshless method, and have been widely applied to production and living. Meshless method gets rid of bondage of mesh and element, and overcomes the shortcomings of traditional methods, such as finite element method and finite difference method. The radial basis function partition of unity collocation method is a new type of meshless method, and based on radial basis collocation as well as partition of unity.This method breaks the whole research domain into some small subdomains, then get the approximate solution of subdomain by radial basis function collocation method. Finally, we get the approximate solution of the whole domain by weighting.The paper based on the radial basis functions and scattered data interpolation, introduces the radial basis collocation method, then combines it with partition of unity for solving the problem of two-dimensional mixing flow of confined and unconfined groundwater. In the process of numerical simulation, construction the algorithm of solving the problem of mixing flow of confined and unconfined groundwater. Compared with other numerical simulation methods, the programming radial basis function partition of unity collocation method is more simper and versatility, above all, the method reduces the computational costs. This paper is composed of four chapters. In chapter 1, we introduce the knowledge groundwater, and conclude two-dimensional groundwater flow equations. In chapter 2, we list the common radial basis functions and its derivatives. In chapter 3, we detail the radial basis function collocation method and combine it with the partition of unity method, then develop the radial basis function partition of unity collocation method. In chapter 4, we apply the radial basis function partition of unity collocation method to the problem of two-dimensional mixing flow of confined and unconfined groundwater. Finally, we conclude the paper and make expectation about the application of the radial basis function partition of unity collocation method in groundwater.