土石坝渗流分析中的Chebyshev谱元法

A Chebyshev Spectral Elements Method for Earth Dam Seepage Analysis

基于谱元法理论,对土石坝一维二维渗流问题进行了理论分析。首先建立了与土石坝渗流微分方程初边值问题等价的积分形式,选取Chebyshev多项式作为函数插值的基函数,得出渗流问题的离散矩阵方程。然后采用与有限元相似的方法集成整体系数矩阵,根据不同的边界条件,最终计算得到结点水头列阵{h},通过谱插值点来求出整个土石坝各点的水头值。

Based on the theory of spectral elements method,this paper theoretically analyzed the issue of earth dam seepage under both one-dimensional and two-dimensional conditions. First, an integral form about the seepage problem was set up; then, the discrete matrix equations were formed by using Chebyshev polynomials as the basis function and the global coefficient matrix was formed in the way used in the finite-element method. Finally,according to different types of boundary conditions,water head linear array { h} was calculated and the whole dam＇s water head was educed from this linear array.