Application Of Element Free Galerkin Method For Confined Flow Of Groundwater

The numerical simulation of groundwater has become an important basis for the development,management and utilization of water resources.At present,the main method of groundwater numerical simulation is finite element method and finite difference method.There are many kinds of simulation software based on these two methods,but these softwares can not solve all the problems of groundwater.For some complex problems,it is necessary to construct a specific algorithm for programming to simulate.Moreover,these methods are based on elements and grids,which bring a lot of inconvenience to the solution of the problem.In the past two decades,a new numerical simulation method,meshless method,which does not require meshes and cells,has been gradually discovered and developed.Meshless square method overcomes many shortcomings of finite element method and finite difference method,among which Element Free Galerkin Method(EFGM)is a representative and influential method.This paper tries to solve the problem of groundwater flow in confined aquifer by this method.The main contents of this paper are as follows:(1)Describing the origin of meshless method and its history,Summarizing the value of groundwater numerical simulation and its progress and the basic principle of EFGM.(2)Aiming at the problem of stable groundwater flow in heterogeneous media,a new method for solving this problem is established by using EFGM and compatibility condition.This method can be regarded as a coupling method of EFGM and collocation method.(3)We apply the EFGM to the well flow problem of confined aquifer,and construct a numerical model to solve the problem.The feasibility of the method in solving the groundwater flow problem is verified by the model trial calculation.(4)Applying the software of MATLAB to the calculation of groundwater flow problem by EFGM,we establish the mathematical model and develop the corresponding program according to the solution of the problem.The program make full use of the advantages of MATLAB programming,programming matrix representation method,so that the developed program is concise and efficient.