Boundary Element-free Method For Solving Steady Flow Problems

In the research category of meshless method,boundary element free method(BEFM)is a newly developed numerical method.BEFM was first proposed by Cheng Yumin et al.,it is based on the principle of combining improved moving least square(IMLS)method with boundary integral equation(BIE)method.This method gets rid of the dependence on mesh division and the restriction of mesh,its essence is a real meshless method and has been got the preliminary application in the field of elastic mechanics.This article is divided into five parts.Part I,it briefly describes the characteristics of traditional numerical methods,including finite difference method(FDM),finite element method(FEM),and boundary element method(BEM),summarizes the development of meshless method and BEFM,sums up the significance and methods of the numerical simulation of groundwater.Part II preparatory knowledge,we introduce moving least square(MLS),IMLS and BIE methods.Part III,the basic principle of BEFM is given,and BEFM is used to calculate typical problems of groundwater steady seepage in homogeneous medium and steady flow in heterogeneous medium,respectively.Part IV,BEFM is applied to the study in confined steady well flow of groundwater,the boundary element free numerical model with group wells and BEFM solution of numerical examples are given.Comparing BEFM solution with BEM solution and exact solution,and analyzing the effect of the selection of the influence domain radius on BEFM solution.Part V,based on the above,the boundary element free numerical model for steady well flow in overflowing aquifer is derived and calculated with a typical example.By analyzing and comparing the simulation results obtained by using BEFM,it can be seen that this method is effective in solving the problem of the steady flow of groundwater,the accuracy of BEFM can reach the standard of BEM,and this method is especially good at dealing with well flow problems.Therefore,BEFM can meet the general needs of groundwater numerical simulation,which provides a new tool for hydrogeological research and groundwater numerical simulation and prediction.