Using Partition Of Unity Collocation Method To Solve The Problem Of Two-Dimensional Unsteady Groundwater Flow

The Meshless method is gradually developed after the traditional method.It is an important numerical method.It gets rid of the bondage of the traditional background grid,overcomes the disadvantages of amount of calculations and inflexible in the finite element method and finite difference method.The partition of unity collocation method is a new meshless method,it is based on radial basis collocation,this method is a true meshless method,not only has a small amount of calculation but also the approximation of the calculated has a high degree of precision.So in recent years,some people gradually try to use the partition of unity collocation method to solve the problem of engineering calculation.The partition of unity collocation method breaks the whole research domain into some small subdomains,and estimates the overall with local,then get the approximate solution of the whole domain by weighting.The coefficient matrix is sparse and flexible.In this paper,for the first application of partition of unity collocation method in solving two-dimensional unsteady groundwater flow problem,using this method to solve the mathematical model,then to establish the corresponding algorithm for solving the problem of two-dimensional mixing flow of confined and unconfined unsteady groundwater.In this paper,the main work is using the partition of unity collocation method to establish the two-dimensional problem of unsteady flow of groundwater numerical simulation model,and using Matlab numerical simulation of groundwater.From the simulation results,compared with the traditional methods,the method error is relatively small and quite satisfactory.This paper is divided into five parts.The first chapter briefly summarizes the research progress and prospects of the development of meshless method in recent years.The second chapter reviews the significance of groundwater flow and the issues of two-dimensional problem of unsteady flow.The third chapter gives the radial basis function,the radial basis function interpolation,the basis principle of partition of unity collocation method,selection of unit neutron domain decomposition collocation method.The fourth chapter is the partition of unity collocation method was applied to solving the practical problems in groundwater of unsteady flow in two-dimensional according to the established mathematical model of concrete corresponding program with Matlab,draw a two-dimensional graphics of underground water and the traditional method of unsteady flow of groundwater level graphical,comparing the contour plot the result accuracy is higher.In chapter 5,finally,thesummary and outlook,after using this method to solve practical problems we conclude the paper and make expectation about the application of the partition of unity collocation method in groundwater.