The Meshless Local Petrov-Galerkin Method Research In Numerical Simulation Of Groundwater

At present,the meshless method has become the focus of researchers. Themeshless local Petrov-Galerkin method (MLPG) is a new numericalsimulation method. It uses local weighted residual method, and its numericalintegral can be in the local domain. For a domain node, its local integral domaincan take rules and simple shapes, and can calculate numerical integral in thelocal domain. For located at or near the complex geometry boundary node,itonly uses local grid, so it does not need the global grid background.This paper analyzes the method of weighted residuals and moving leastsquares (MLS) shape function through solving differential equations, fromMLPG method and MLS shape function, constructs meshless localPetrov-Galerkin method of groundwater two-dimensional steady flow andtwo-dimensional unsteady flow, researches MLPG algorithm steps of the two-dimensional steady flow, and draws the flow chart of program structure.Then it solves head calculation of groundwater steady flow problems andunsteady flow problems using the meshless local Petrov-Galerkin method, andprograms using Matlab language for calculation. The results show that themeshless local Petrov-Galerkin method has higher calculation precision, and itcan be used for science and numerical simulation of groundwater engineeringdesign.In this paper, results of researching on the meshless local Petrov-Galerkinmethod will contribute to further study of numerical simulation of underground.