Solve The Quasi Three-dimensional Problem Of Groundwater Flow By Using The Element-free Galerkin Method

The meshless method has been a hot direction and the development trend of numerical methods in recent years at home and abroad. Element- free Galerkin(EFG) method is one of the meshless methods, which is most widely researched and applied. In EFG the shape function is constructed by the moving least square approximation, then through deal with essential boundary conditions and gets the Galerkin equal form of differential equation.Firstly, the paper systematically introduces the background knowledge and present development of meshless method and the significance of numerical simulation of groundwater. The paper gives a presentation of the moving least square approximation, weighting functions, calculation of derivatives of shape function matrix LU, the domain of calculation points.Secondly, introduce the meshless Galerkin method with the method of weighted residuals, and from a practical application-groundwater flow, the basic equations of the two-dimensional steady flow and unstable flow problem were derived by EFG respectively. The meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, and point out its special methods. Furthermore, error estimates of EFG are analyzed. From the error analysis, it is shown that the error of numerical solution is directly related to the radii of weight functions.Lastly, solve a quasi three-dimensional model of groundwater flow by using the element-free Galerkin method and get its equation of Galerkin. Draw up the procedure of MATLAB and analyse the numerical. The calculation shows that the EFG method is reasonable and has many virtues, such as high precision ,easy handling and so on.