有自由面渗流分析的三维数值流形方法  

Three-dimensional numerical manifold method for seepage problems with free surfaces

作　　者：姜清辉[1,2] 邓书申[2] 周创兵[2] 

机构地区：[1]武汉大学土木建筑工程学院,武汉430072 [2]武汉大学水资源与水电工程科学国家重点实验室,武汉430072

出　　处：《岩土力学》2011年第3期879-884,共6页Rock and Soil Mechanics

基　　金：国家自然科学基金项目(No.50839004;No.51079110);教育部新世纪优秀人才支持计划项目(No.NCET-07-0632)

摘　　要：提出了求解有自由面渗流问题的三维数值流形方法,通过构造任意形状流形单元的水头函数,推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程,并给出了自由面的迭代求解策略和渗透体积力的计算方法。典型算例的数值分析表明,该方法采用数学网格覆盖整个材料区域,在自由面的迭代求解过程中数学网格保持不变,只考虑自由面以下渗流区的介质,只对自由面以下的流形单元形成总体渗透矩阵,具有精度高、收敛速度快、编程简单等优点,而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力,因此,特别适用于有自由面渗流问题的模拟。A three-dimensional numerical manifold method for seepage problems with free surfaces is proposed.The hydraulic potential functions for arbitrarily shaped manifold element are constructed and the element conductivity matrix is derived in detail.The global governing equations for unconfined seepage analysis are established by minimizing the flow dissipation energy.The proposed method employs the tetrahedral mathematical meshes to cover the whole material volume.In the process of iterative solving for locating the free surface,the numerical manifold method can strictly realize the seepage analysis of the saturated domain on the condition of mathematical meshes keeping unchanged.Furthermore,the seepage force acting on the transitional elements cut by the free surface can be accurately calculated by the manifold method.Therefore,the proposed method is featured in high accuracy,fast convergence rate and simple programming,especially applicable to simulate the unconfined seepage problem with free surface.

关 键 词：三维渗流 数值流形方法 自由面 数学网格 流形单元 

分 类 号：O342[理学—固体力学]