Boundary Element-free Analysis Of Confined Steady Well Flow

The boundary element-free method is a meshless boundary integral equation method,which combines the improved moving least square method with the boundary integral equation,and then obtains the numerical solution of partial differential equations.In this paper,the boundary element-free method is applied to solve the problem of groundwater flow,and the boundary element-free numerical model of groundwater flow in confined aquifer is established.Based on the boundary integral equation,the numerical simulation of process groundwater flow is presented.A numerical model of two-dimensional steady well flow is established,and a boundary element-free formulation for the steady flow problem of well group is derived,and the boundary element-free method for solving the problem of well group is discussed.Here is based on the boundary integral equation,the orthogonal function family with weight is chosen as the basis function of the moving least square method.The moving least square method is used to construct the approximation function of water head on the boundary,coupled with the boundary integral equation.The dispersion of boundary integral equation of the boundary element-free method for groundwater flow in confined aquifer the is realized.The boundary element-free method is used to solve the boundary problem in homogeneous and heterogeneous media in confined aquifer.In the heterogeneous medium water basin,water basin segmentation into different regions,each region is considered relatively homogeneous.The function of water head and the directional derivative on both sides of the common boundary of the region satisfy the compatibility condition.The nodes are arranged on the outer boundary and inner boundary of each region,and the integral equation of the boundary element-free method is added to obtain the linear equation set for solving the problem of groundwater flow in confined aquifer,and then solve the unknown value.In the stable groundwater flow model of well group.When there is a group of wells(pumping well or water injection well)in the water basin,the boundary of solution domain is extended to the boundary of the river basin and the boundary of wellbore.The boundary node is arranged on the two kind of boundary,an approximation function on the boundary with the improved moving least squares approximation,the boundary integral equation of the boundary element-free method for well group problem is obtained.The boundary points are substituted into the integral equation,the solution of the equation is obtained and then the value of the water head function or the directional derivative of the boundary point is obtained.The boundary element-free method is applied to solve the problem of the steady flow of groundwater in well group in the confined aquifer,and the calculation is completed by Matlab programming.An example shows that the boundary element-free method has high accuracy.This method is significantly lower than the boundary element method on the difficulty of implementation.