The Least-square Collocation Meshless Method In The Groundwater Simulation

Although meshless method has just started, it has become the focus of scientificresearches at home and abroad. Thanks to not relying on grids, there are less difficulties out ofgrid distortion. By taking information of nodes only, it is easier to analyze complexthree-dimensional patterns without the help of grid information. The radial basis function,as akind of meshless method is a way of working out approximate function by taking the radialfunction as the basic function. Collocation Meshless method with radial basis is a new kind ofnumerical simulation method and there are few reports about it in the application ofhydrological geology at home and abroad.By analyzing the least-square method for dealing with differential equations, this papersolve the basic way of using the collocation method for Radial basis function to formfunctions, starting from the collocation method and radial point interpolation shape functionpoint, With it as the basic, we have drawn the formulas for two-dimensional problems byusing the least-square method, formed the least square collocation method of meshlessmethod for groundwater two-dimensional steady flow and unsteady flow, explained thederiving formulas of working out two-dimensional steady flow and unsteady flow by usingthe least square method, and given out the solving process about working with the help of theleast square method.And based on it, we’ve drawn the corresponding flow chart of programstructure. In this paper, the least square collocation method was used in the two-dimensionalsteady flow and unsteady groundwater flow problems head calculation, and there aresatisfactory results by using Matlab language programme. The result of examples has beenpresented by charts more intuitively, And the results show there are better calculation resultsin the least-square collocation Meshless Method rather than Meshless method with. It showsthat the least-square collocation method not only can improve the calculation accuracy, butalso has strong adaptability. It can provide a reference for the engineering design ofgroundwater in Engineering Mechanics.This paper has given out detailed calculation processes for the least square collocationmethod to solve the differential equation a meshless local radial point interpolation method’sresults The project in this paper will promote the development and research of the meshlessmethod by studying the collocation method.