摘要
用传统的有限元方法求解复杂边界的自由面渗流是很困难的,为此提出了基于适体坐标变换的有限差分法。该方法通过求解Poisson方程自动生成计算区域的曲线网格,并将其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。这种数值网格生成技术可以精确而有效率地模拟复杂几何边界,算法成熟,通用性强,可以避免有限元法的网格在迭代过程中变化的问题,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,基于适体坐标变换的有限差分法计算结果的精度和有限元法相当,但计算效率上较有限元方法有很大的提高,并具有简单、灵活的优点。
The traditional fixed meshes used in the finite element method (FEM) for seepage analysis with free surface involves modifications of the mesh as the free surface changes. A finite difference method was developed using boundaryfitted coordinates to simplify the analysis. The boundary fitted coordinates were constructed by solving the Poisson equation with the grid lines coincident with the irregular physical boundaries, thus greatly simplifying the implementation of the boundary conditions. The main advantages for the free surface seepage analysis are accurate implementation of the moving free surface and the ability to construct a generalized computer code which can be consistently applied to physical domains of any shape. Case studies show that the method yields satisfactory results and is much more efficient than the traditional FEM.
出处
《清华大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2003年第2期273-276,284,共5页
Journal of Tsinghua University(Science and Technology)
基金
国家自然科学基金会
长江水利委员会联合资助项目(50099620)
