Study On EFG Algorithm For Soil Solute Transport Equations

Meshless method,the new numerical method developed in recent years,mainly through local support node and shape function in domain,achieves numerical calculation of global scope.Since this method does not rely on the mesh information,we can completely eliminate the difficulties brought by meshing.Compared with FEM,it owns significant advantage in dealing with the problem of large deformation,crack propagation and dynamic discontinuous boundary.Element free Galerkin(EFG)algorithm is one major branch of meshless method which is important on science and engineering computing.Now,it is widely used.This paper,therefore,focuses on the characteristics of EFG algorithm.Combining with soil solute transport background,we offer a more comprehensive analysis.The effectiveness of this algorithm is clearly demonstrated by error analysis.Main points of this paper are as follows:Firstly,we analyze the existing theories of meshless algorithm and EFG algorithm: Based on the study of relevant soil solute transport equation of domestic and foreign literature,and the understanding of EFG algorithm,the background,scientific significance and application prospects of this article are provided.Besides,we find out that to obtain an algorithm with lower error,higher accuracy,and better convergence is still a tough problem for soil solute transport equation.After in-depth study of EFG,we realize that this theory is still suitable for soil solute transport equation.Followed by the implementation procedure of EFG algorithm,we emphatically introduce the derivation of soil solute transport equations of EFG method.Secondly,we propose an error estimation method based on soil solute transport equations: By oval projection operator,and in conjunction with mobile least squares interpolation error estimates sobolev space,the semi-discrete soil solute transport equations Element free Galerkin algorithm and full discrete priori error estimates are offered in this paper.The semi-discrete error obtained from error estimation equation is related to the radius of influential domain of weight function.The fully discrete error is related not only to the radius of influential domain of weight function but also to its time step.Thirdly,numerical simulation for one-dimensional,two-dimensional problem of soil solute transport equations is provided.The simulation results illustrate that the algorithm proposed in this paper is of higher accuracy and better convergence,compared with conventional finite difference method,finite element method.That is to say,this method is an effective calculation method,Finally correctness of the error estimates are verified as well,namely,calculation error decreases as the space step and the radius of the influence domain decrease,When radius of influence in power and space step are fixed,the smaller the time step is,the lower calculation error is.