基于van Genuchten-Mualem模型的饱和-非饱和介质流动随机数值分析

基于van Genuchten-Mualem非饱和水分特征模型，联合运用Karhunen-Loeve展开法、混沌多项式展开以及摄动方法，对饱和-非饱和流问题进行随机数值分析。将土壤特性参数假定为协方差已知的随机函数，并按Karhunen-Loeve法分解，把压力水头表示为多项式。通过摄动方法得到一系列关于水头展开式的偏微分方程，用有限差分法进行求解，获得了压力水头的随机描述，并计算其均值和方差。应用本文的随机模型研究了二维非饱和以及饱和-非饱和介质流动的实例，结果与动量方法的计算结果一致，而且计算效率高于传统的动量方法。

Stochastic numerical analysis of flow in saturated-unsaturated porous media based on van Genuchten-Mualem model

On the basis of van Genuchten-Mualem constitutive relationship the stochastic numerical analysis of saturated-unsaturated flow in porous media is carried out. The soil parameters are assumed to be normal random functions with known covariance and decomposed by Karhunen-Loeve expansion. The pressure head is expressed as polynomial chaos expansion and using the perturbation method to establish a series of partial differential equations in which the dependent variables are the deterministic coefficient. The equations are solved by finite difference method and the mean and variance of pressure head are determined from its random expression. The proposed stochastic model is applied to investigate some examples of unsaturated and saturated-unsaturated flow in porous media and the results are compared with those derived from momentum-based stochastic model. Good agreement is obtained and the proposed model is computationally more officient.