Boundary Element-free Method For Variable Coefficient Seepage Problems

The boundary element-free method(BEFM)is one of the meshless methods.It is a new method for constructing the numerical solution of the differential equation problem by combining the improved moving least squares and the boundary integral equation.The most remarkable feature of this method is that it does not need to divide the element or the grid,as a result,there is growing concern.Firstly,the historical background of numerical simulation of seepage flow,the historical application and development of boundary element method(BEM)and boundary element-free method(BEFM)are summarized,the basic principles and methods of the moving least squares,the improved moving least squares and the boundary integral equation are expounded,and the boundary element method(BEM)is summarized.Based on the above,the main work of this paper is to solve the variable coefficient seepage problem by boundary element-free method.In this paper,the boundary element-free method is established when the seepage coefficient is a function,and the boundary element-free method is used to solve the variable coefficient seepage problem.The whole study area is divided into several sub-regions,and the permeability coefficient is approximately expressed as a constant in each sub-region,using the improved moving least squares to construct the head approximation function and the flow approximation function,a boundary element free algorithm is generated to solve the head approximation and the flow approximation on the boundary node,then,the approximate solutions of water head and flow are obtained by the boundary element-free Algorithm corresponding to the interior nodes.According to the boundary element-free Algorithm given in this paper,the MATLAB Program is compiled and the calculation of two kinds of seepage problem is completed.In the process of programming,according to the characteristics of MATLAB language,a large number of matrix programming method is used,which greatly reduces the programming workload and improves the efficiency of numerical simulation.The results show that the boundary element-free method(BEFM)is more accurate and easier to implement than BEM.