Application Of Element Free Galerkin Method For Simulation Of Groundwater

Numerical simulation of groundwater flow has been commonly based on traditional methods such as Finite Element Method and Finite Difference Method.It is necessary to construct grids.These mesh-based methods require computational grids,which can be costly to generate,increase the difficulty of algorithm and reduce the flexibility of solving problems.In recent years,more and more researchers are trying to find a new method that only needs to lay out nodes,without grids and cells.Element Free Galerkin Method avoids the construction of grids or elements,reduces the processing work in the early stage of numerical simulation.This method can flexibly arrange nodes,and it is easy to understand the algorithm.The accuracy of calculation results are high,so it provides a new method for the workers engaged in groundwater simulation.Element Free Galerkin equation are derived to solve two-dimensional steady and unsteady flow in confined aquifer in this paper.The Improved Moving Least Square Method is used to construct the shape function which only depends on the nodes,the selection principles and types of the weight function are discussed.The integral weak form of the flow model are derived.The reason why it is difficult to impose the essential boundary conditions in meshless method are explained.The application methods are described in detail by taking the Lagrange multiplier method,penalty function method and FE-EFG coupling method as examples.In order to solve the integral terms in the linear equations of head function,the background lattice integration method,background grid integration method and node integration method are introduced.A coupling algorithm of Element Free Galerkin Method and Point Collocation Method is established to solve confined steady flow of unhomogeneous problems in groundwater.Based on the compatible conditions of water head and rate of flow,a set of equations are established by using the method of collocation on the nodes of dividing lines of different zones;Galerkin equations without element are established on the sub areas where the dividing lines are removed in each zone,and the coupling equations for solving the numerical solution of water head function are obtained by combining.For a specific example,trying to program the solution,and the numerical solution obtained are compared with the accurate solution and the solution of Boundary Element Method.The results show that the accuracy of the above method is high,so it provides a new and effective method for solving this kind of problem.Element Free Galerkin Method is applied to solve the two-dimensional unsteady flow problems in unconfined aquifers.The Element Free Galerkin equation for solving this kind of problems is derived,and the algorithm based on this equation is given.Numerical examples show the effectiveness and feasibility of this method.