CAJ | 학술논문

　　岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题，提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域，该方法通过将不规则求解区域嵌入一个正则矩形区域，在正则区域上采用重心拉格朗日插值近似未知函数，利用配点法离散渗流问题的控制方程，将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散，通过置换方程法和附加方程法施加边界条件，利用正则区域上的重心插值配点法，通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。
　　암토체적삼투파배、지하공정적방삼설계등무불여삼류계산유관。침대삼류자유면문제，제출일충중심랍격랑일삽치적배점형무망격방법。유우삼류자유면문제적구해구역시불규칙구역，해방법통과장불규칙구해구역감입일개정칙구형구역，재정칙구역상채용중심랍격랑일삽치근사미지함수，이용배점법리산삼류문제적공제방정，장중심랍격랑일삽치적미분구진리산성대수방정표체적구진형식。장자유면상적변계조건통과중심랍격랑일삽치리산，통과치환방정법화부가방정법시가변계조건，이용정칙구역상적중심삽치배점법，통과질대학정최종자유면적위치。수치산례표명소제출적무망격방법대우구해삼류자유면문제적정학성화고정도。
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.