关键词: 渗流自由面问题, 无网格方法, 重心拉格朗日插值, 微分矩阵, 配点法, 正则区域法

Abstract: The seepage failure of rock and soil and the seepage design for underground engineering are closely related to the seepage calculation. A meshless collocation method based on barycentric Lagrange interpolation for solving seepage free surface problems in 2D is presented. Embedded the irregular seepage domain into a regular rectangular domain, the seepage governing equation is extended into the regular rectangular domain. The unknown function of seepage in seepage domain is approximated by barycentric Lagrange interpolation in regular rectangular domain. Then, the barycentric Lagrange interpolation collocation method (BLICM) can be used to solve seepage problems in the regular rectangular domain. The governing equation of seepage problem is discretized by using BLICM into algebraic equations. Using notations of differentiation matrix and Kronecker product of matrices, the system of algebraic equations can be rewritten as matrix form. The boundary conditions are discretized by barycentric Lagrange interpolation and applied by using replacement equation method or/and additional equation method. The final location of free surface is obtained by iteration computation of BLICM in regular rectangular domain. The numerical results compared with others numerical methods indicate the correctness and high accuracy of the proposed method.

Key words: seepage free surface problem, meshless method, barycentric Lagrange interpolation, differentiation matrix, collocation method, regular domain method