Application Of The Least Square Collocation Method In Calculation Of The Two-dimensional Profiling Engineering Groundwater

The meshfree method has become a research hotspot of scholars both at home andabroad, mainly because: in meshfree method, the application of the trial function is not basedon the grid. Therefore, in dealing with large deformation, fluid-structure interaction and thefree surface flow problem is related to embody its superiority. Least squares collocationmethod and radial basis function collocation method have a lot of similarities. It retains somethe advantages of the radial basis function collocation method: no need to reconstruct meshsubdivision, the study area, reduce a large of data preparation work; also overcome some ofits insufficient problems, because it only within the computational domain node, sometimescalculation result is not very ideal, and the least square collocation method not only decoratein the computational domain node, add the support points, the precision of calculation result ishigher than its result. Therefore the results of practical problems calculated by the leastsquares collocation method have more practical and investigative value.The focus of this article is applying the least square collocation method totwo-dimensional profiling engineering groundwater. The first chapter introduces thedevelopment background, history, and advantages and disadvantages of the meshfree method;and points out the main investigative problem in this paper. The second chapter discussessome theoretical knowledges related to the least squares collocation method.Firstly introducesthe definition of radial basis function and the interpolation theory; then with aone-dimensional model of unsteady flow of groundwater as an example, discusses the basictheory of least squares collocation method.The third part generalizes the groundwatercalculation in the engineering aspects of flexible use of least squares collocation method andsome related problems in the groundwater numerical simulation processing, such as modelselection, the processing of boundary condition, the profiling model, unsteady flow problems,and so on; Then calculated four practical examples, solve the plane of one-dimensional andtwo-dimensional profiling problems. As can be seen from the calculation results, the leastsquares collocation method applied in groundwater numerical simulation of thetwo-dimensional profiling problems is very effective. The fourth part of the whole paper issummarized and look ahead of the development of the least square collocation method.