| In recent years, the Meshless Local Petrov-Galerkin Method (MLPG) has beendeveloping significantly in solving partial differential equations. It only uses local weak formon the local sub-domain, the trial function and weight function are chosen from differentspaces, doesn’t require background cell, which overcomes dependence on the cell of thetraditional methods.It is truly meshless method. In these cases, this paper applied MLPG tothe numerical simulation in groundwater field, as well as used this method to calculate steadyflow model.In this paper, two-dimensional pressure and non-pressure mix of steady flow for theselection of MLS shape functions constructed MLPG groundwater model and developed theprogram of the numerical model by using Matlab. The results show that MLPG is efficiencyand rationality. Besides, this paper combined RBF interpolation with local weak form forsolving the one–dimension steady flow model. The results indicate that this method has highaccuracy, adaptability and others. It is very promising in science and engineering computing.Thesis consists of five chapters. In chapter1, firstly, we describe in detail the produceprocess and the current development of the meshless. Secondly, the significance of thenumerical simulation of groundwater is written. In Chapter2，we mainly give out two kindsof function spaces i.e. Moving Least Square fitting and Radial Basis Function interpolation. InChapter3, we introduce the basic principle of MLPG and the imposition of first boundaryconditions. In chapter4, we apply the MLPG to one–dimension steady flow simulationmodel, compared with the exact solutions. In chapter5, based on the identified hydrogeologyconditions of the research region, we deduce the MLPG numerical model in thetwo-dimensional stable groundwater problem; draw up the corresponding program. Theresults shows the advantage of this method is the high precision and easy to implement.Finally, we make a summary of the MLPG, give out some meaningful conclusions. |
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