Study Of Groundwater Simulation Based On MLPG Method

At present,finite element and finite difference methods are still commonly used in numerical simulation.Such methods require the construction of grids or cells,which brings trouble to the problem solving.In order to overcome such difficulty,meshless method has been developed and attracted more and more attention.The node arrangement of such method is flexible,without grids information,partly or completely avoiding the influence of grids,which is helpful to promote the progress of numerical simulation technology.Among these methods,meshless local Petrov-Galerkin(MLPG)method combines Petrov-Galerkin method with meshless approximate function,which is a pure meshless method without grids either in the process of shape function construction or numerical integration.This paper first summarizes the development history of meshless method and MLPG method.Introduces the weighted residue method as the basis of MLPG method,the moving least square method for constructing approximate solution function and two methods for applying essential boundary conditions are introduced.Secondly,aiming at the common groundwater simulation problem in which the permeability coefficient is a shard constant,a coupling solution method of MLPG method and collocation point method is established to solve this kind of problem.The method according to the characteristics of the permeability coefficient of piece-wise constant,and collocation method points area set up based on the MLPG method is used to solve the equations,was established in each area to remove the boundary nodes MLPG equations,on the node of each line layout,application compatibility equations with the conditions,and solving the problem have been obtained numerical solution of the coupled equations about the head,the algorithm of solving the equations is given.The results are compared with those of MLPG method and BEM method,and the results show that this method has higher accuracy.Then,the MLPG method is used to solve the steady flow problem of unconfined groundwater.The MLPG method for solving the steady flow problem of unconfined groundwater is established.On this basis,the method is applied to solve the steady flow problem of a complete well with constant drawdown in unconfined aquifer.The MLPG method for the steady flow problem of unconfined aquifer in the form of polar coordinates is derived,and an iterative method for solving the nonlinear MLPG equation is given according to the linearization method.A numerical example is given to verify the effectiveness of the method.Finally,the MLPG method is used to solve the unsteady flow problem of unconfined groundwater.The MLPG method for the unsteady flow of unconfined groundwater is derived.On this basis,the method is used to solve the unsteady flow problem of a complete well with constant flow rate in an unconfined aquifer.The MLPG implicit scheme for the steady flow problem of complete Wells with constant flow rate in unconfined aquifer in polar coordinates is derived.A numerical example is given to verify the feasibility of the method.