Applying the Radial Basis Function Collocation Method to Solve Steady Flow Problems

Abstract: Meshless method is a newly developing numerical method in solving partial differential equations. Based on the point approximation, the meshless method can eliminate meshes partially or completely, thus reduce the computational time. Meanwhile, it maintains the solution accuracy. Radial basis function collocation method is a truly meshless method and easy-to-program. In this dissertation, we firstly introduce the basic theory of the meshless method. And then, we narrate the fundamental theory of the Multi-quadrics (MQ) collocation method and apply this method to solve steady flow problems encountered in heterogeneous porous media. The outline of the dissertation is as follows. In chapter one, we summarize the background, current research and future tendency of the meshless method. In chapter two, we outline the MQ collocation method and use this method to solve poisson problems. Followed by chapter 4, the MQ collocation method is applied to simulate groundwater problems. According to our numerical examination in solving two dimensional steady flow problems in heterogeneous porous media, we analyze the sensitivity of the solution accuracy to the nodes distribution and shape parameters. The numerical simulation for three dimensional steady flow problems in heterogeneous porous media is also investigated. Finally, conclusions and prospect are given in chapter five…
Key words: radial basis function; collocation method; porous media; steady flow; simulation in groundwater

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