Gaussian Closure of One-Dimensional Unsaturated Flow in Randomly Heterogeneous Soils |
| |
Authors: | Amir Orna Neuman Shlomo P |
| |
Institution: | (1) Program in Applied Mathematics, University of Arizona, Tucson, AZ, 85721, U.S.A.;(2) Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ, 85721, U.S.A. |
| |
Abstract: | We propose a new method for the solution of stochastic unsaturated flow problems in randomly heterogeneous soils which avoids linearizing the governing flow equations or the soil constitutive relations, and places no theoretical limit on the variance of constitutive parameters. The proposed method applies to a broad class of soils with flow properties that scale according to a linearly separable model provided the dimensionless pressure head has a near-Gaussian distribution. Upon treating as a multivariate Gaussian function, we obtain a closed system of coupled nonlinear differential equations for the first and second moments of pressure head. We apply this Gaussian closure to steady-state unsaturated flow through a randomly stratified soil with hydraulic conductivity that varies exponentially with where =(1/) is dimensional pressure head and is a random field with given statistical properties. In one-dimensional media, we obtain good agreement between Gaussian closure and Monte Carlo results for the mean and variance of over a wide range of parameters provided that the spatial variability of is small. We then provide an outline of how the technique can be extended to two- and three-dimensional flow domains. Our solution provides considerable insight into the analytical behavior of the stochastic flow problem. |
| |
Keywords: | gaussian closure unsaturated flow random heterogeneity stochastic equations |
本文献已被 SpringerLink 等数据库收录! |
|