文档介绍：摘要内容摘要:无网格局部彼得罗夫一伽辽金(MLPG)法是一种偏微分方程数值求解的新方法。该方法在对微分方程数值离散时不需要网格,因此不仅避免了生成网格的复杂过程, 而且消除了传统网格方法(如有限元法、有限差分法等)中因网格畸变带来的不利影响, 是真正的无网格数值方法。本文概括了MLPG方法的主要原理,并将这种方法应用于求解非均质多孔介质中的水流问题。全文共分五章。第一章主要总结了无网格方法及 MLPG法近年来的发展和研究现状。第二章是预备知识,首先介绍了求解偏微分方程的加权残量法,然后概述了本文建立的MLPG法的近似方案——移动最小二乘近似。第三章对二维地下水稳定和非稳定流的MLPG方程进行了推导。第四章将MLPG法用于地下水数值模拟中,用MLPG法对水文地质参数按函数连续变化、渐变和突变3种非均质多孔介质中的二维地下水稳定流、非稳定流分别用MLPG和有限元法进行了计算,得到了满意的结果。第五章对MLPG法进行了总结与展望。关键词:局部Petrov-Galerkin方法,移动最小二乘法,多孔介质,非均质,地下水数值模拟 Abstract Content:The Meshless Local Petrov—Galerkin Method(MLPG)is atruly meshless numerical method insolving partial differential does not need mesh any more intheprocess ofdiscretizing governing equations,therefore,the drawbacks encountered inthetraditional mesh—based methods(such asthefiniteelement method and thefinitedifference method)is thisdissertation,we recapitulate themain theory oftheMLPG andapply this method to solve the current problem ofporous media ingroundwater paper consists chapter 1,we summarize thehistoryand thedevelopment ofthe meshless method especially 2includes thepreliminary firstreview animportant andefficient method insolving partial differential equation····-·the Weighted Residual Methods,and then theMoving Least Square approximation ispresented. Followed by Chapter 3,we deduce theMLPG governing equations forstableand unstable groundwater intwo chapter 4,the MLPG is applied to simulate the groundwater problems,that is,steady flowandunsteady flowinheterogeneous porous media with three kinds of hydro-geological parisons are made with the finite element results show that the MLPG isbetter than the traditional mesh—based methods intheaspects putation and solution thelastchapter, someconclusions and prospects oftheMLPG aregiven. Key words:Local Petrov·Galerkin method(MLPG),moving leastsquare method,porous media,heterogeneous,numerical simulation ofgroundwater 学