基于KL-Galerkin解法的地下水流动随机分析  

Stochastic Analysis of Subsurface flow Based on KL-Galerkin Method

作　　者：史良胜[1] 杨金忠[1] 李少龙[1] 林琳[1] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,武汉430072

出　　处：《四川大学学报（工程科学版）》2005年第5期31-35,共5页Journal of Sichuan University (Engineering Science Edition)

基　　金：国家自然科学基金资助项目(50379042)

摘　　要：为处理二维一般区域和具有复杂协方差函数的地下水流动随机问题,需要提出有效数值方法以求解基于摄动理论的谱分析模型。建立了进行K-L(Karhunen-Loeve)展开的Galerkin有限元方法,推导出任意区域K-L展开和Fredholm方程的矩阵形式和变换公式,研究了KL-Galerkin解法的计算性态。将基于KL-Galerkin解法的水流随机模拟得到的结果与解析解法的结果进行了对比。计算结果表明:文中提出的算法能够准确的模拟含水层中水头、含水量等物理量的分布,同时由于引入有限元原理和数值积分,该算法能够求解二维一般区域和任意协方差函数的随机场问题。A numerical approach should be developed for spectral model based on perturbation method in the stochastic analysis of subsurface flow with arbitrary domain and complex kernel. The authors proposed a Galerkin finite element method, and derived matrix expression and transformation formulae of Fredholm equation and K-L expansion. Some properties are revealed about KL-Galerkin method. The results from KL-Galerkin-based model are compared with those from analytical solution. It shows that stochastic analysis of subsurface flow based on our proposed method can simulate the distribution of the head and water content accurately. The method is applicable in irregular domain and for any covariance function because of the introduction of the finite element theory and numerical quadrature method.

关 键 词：地下水 随机场 Karhunen-Loeve展开 特征值 特征函数 

分 类 号：TV131.4[水利工程—水力学及河流动力学]