李群方法在渗流力学的应用  

Application of Lie Group to mechanics of fluid flow in porous media

作　　者：侯绍继 刘曰武[1] 李奇[1] 

机构地区：[1]中国科学院力学研究所流固耦合实验室,北京100190

出　　处：《纯粹数学与应用数学》2016年第4期399-408,共10页Pure and Applied Mathematics

摘　　要：试图用李群方法来分析流体及渗流的运动规律.对于流形上流体、渗流力学方程的研究,物理空间的流动中的拓扑结构只要具有李群的性质,便可以此来进行流动分析.这是将李群理论直接、直地应用于渗流力学的一种方法.李群方法将众多求解特定类型的渗流微分方程方法统一到共同的概念之下.李群无穷小变换方法为寻找微分方程的闭合形式的解提供的广泛的应用,补充了求解渗流力学方程的数学物理技巧.Try to use Lie group methods to analyze the fluid and the fluid in porous media. For the fluidmechanics and fluid mechanics in porous medium research on the manifold, if topological structure of the flow ofthe physical space has the nature of Lie groups, we can analyze the flow. This is the theory of Lie groups directlyapplied to fluid mechanics. Lie group method of solving a specific type of differential equation method unifiedunder the concept of the common. In fact, Lie group infinitesimal transformation method for the closed-formsolution of ordinary differential equation with the wide application of technique, when it is applied to the partialdifferential equation, the method of Lie group can export symmetrical to obtain the exact solutions for partialdifferential equations. The mathematical physics technique for solving the equation of seepage flow is added.

关 键 词：李群 渗流 隔开 偏微分方程 无穷小变换 

分 类 号：O035.73[理学]