用适体坐标变换方法求解渗流

运用传统的有限元方法求解渗流问题时,需要人为进行网格划分等前处理工作。当问题涉及自由变动边界时,求解比较困难。本文将适体(Boundary Fitted)坐标变换方法用于岩土工程渗流计算。通过求解Poisson方程自动生成贴合实际物理边界的计算网格,并将渗流问题变换至规则统一的直角网格系统下进行有限差分离散和数值求解。对不同的几何边界可以实现统一的数值求解算法,自动化程度高。计算实例表明,这种方法具有简单、快捷的优点,生成的网格质量较高,是一种很有意义的方法。

Seepage analysis by boundary-fitted coordinate transformation method

The traditional finite element method (FEM) involves constructing mesh by hand,and the computation is complex when the analysis relates to seepage with free surface. In this paper, the finite difference method (FDM) based on the boundary-fitted coordinate (BFC) transformation is presented. The curvilinear grid system, with computational boundary coincident with the physical boundary, is numerically obtained by solving the Poisson equation. The seepage analysis is then done by FDM in a uniform transformed Orthogonal Coordinate system, and a uniform computer code is compiled which can be consistently applied to problem in domain of any shape. Case studies showed that the method could get satisfactory results and was more efficient than traditional FEM.