Application Of Non-symmetric Radial Basis Function Collocation In Simulation Of Groundwater Flow

The meshless method is a newly developing method in solving numerical value in recent years. As it does not rely on the grid, this method can avoid the influence of the mesh distortion on the finite element method and the finite difference method. Now the most popular methods of the meshless method are the Element-free galerkin method and the radial basis function collocation method. The Element-free galerkin method needs the numerical integration and the grid, the calculation is complex, it is not the truly meshless method in fact. On the other hand, the radial basis function collocation method can eliminate the meshes completely, it is a truly meshless method. Comparing with the Element-free galerkin method, the radial basis function collocation method has higher efficiency and accuracy.In this dissertation, we investigate the basic theory of the non-symmetric radial basis function collocation method, and apply this method to the numerical simulation in groundwater field. There are five sections in this paper. In section 1, we summarize the background, history and the development of meshless method. Then the major research in this dissertation is introduced. Section 2 includes the preliminary knowledge. In this section, the method of radial basis function is introduced. In section 3, we introduce the theory of non-symmetric radial basis function collocation method.In section 4, we apply this method to the numerical simulation in groundwater field. Firstly, we solve the problem of the two-dimensional steady groundwater flow in three kinds of parameters. Secondly, the problem of the two-dimensional unsteady flow is solved. In the last of this section, the numerical simulation for three-dimensional steady groundwater flow is investigated. In section 5, we summarize and look forward to the future of the non-symmetric radial basis function collocation method.