Gaussian Finite Element Closure of Steady State Unsaturated Flow in Randomly Heterogeneous Soils

Persistent Link:
http://hdl.handle.net/10150/195087
Title:
Gaussian Finite Element Closure of Steady State Unsaturated Flow in Randomly Heterogeneous Soils
Author:
Wang, Donghai
Issue Date:
2005
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this study, I develop a Gaussian Closure method to simulate steady state unsaturated flow in randomly heterogeneous soils. I predict pressure heads and fluxes and evaluate uncertainties associated with these predictions, without resorting to Monte Carlo simulation, upscaling, or linearization of the governing flow equations and the constitutive relationship between unsaturated hydraulic conductivity and pressure head. Upon treating dimensionless pressure head as a multivariate Gaussian function in the manner of Amir and Neuman [2001], I obtain a closed system of coupled non-linear differential equations for the first and second moments of pressure head and flux for both spatially uncorrelated Y (log saturated hydraulic conductivity) and spatially correlated Y. Computational examples for unsaturated flow in a vertical plane, subject to deterministic forcing terms including a point source, show a good agreement between my Gaussian closure solution and a more general Monte Carlo solution. The computational examples include a uniform domain, eight subdomains, spatially uncorrelated non-uniform Y cases, spatially correlated Y cases, and conditional Y cases. Though the computational examples treat the random pore size parameter a as being uniform across the entire flow domain, I show theoretically that the Gaussian closure method could apply to spatially variable a statistics.
Type:
text; Electronic Dissertation
Keywords:
STOCHASTIC; UNSATURATED FLOW; HETEROGENEOUS SOILS
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Hydrology; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Neuman, Shlomo P.
Committee Chair:
Neuman, Shlomo P.

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleGaussian Finite Element Closure of Steady State Unsaturated Flow in Randomly Heterogeneous Soilsen_US
dc.creatorWang, Donghaien_US
dc.contributor.authorWang, Donghaien_US
dc.date.issued2005en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this study, I develop a Gaussian Closure method to simulate steady state unsaturated flow in randomly heterogeneous soils. I predict pressure heads and fluxes and evaluate uncertainties associated with these predictions, without resorting to Monte Carlo simulation, upscaling, or linearization of the governing flow equations and the constitutive relationship between unsaturated hydraulic conductivity and pressure head. Upon treating dimensionless pressure head as a multivariate Gaussian function in the manner of Amir and Neuman [2001], I obtain a closed system of coupled non-linear differential equations for the first and second moments of pressure head and flux for both spatially uncorrelated Y (log saturated hydraulic conductivity) and spatially correlated Y. Computational examples for unsaturated flow in a vertical plane, subject to deterministic forcing terms including a point source, show a good agreement between my Gaussian closure solution and a more general Monte Carlo solution. The computational examples include a uniform domain, eight subdomains, spatially uncorrelated non-uniform Y cases, spatially correlated Y cases, and conditional Y cases. Though the computational examples treat the random pore size parameter a as being uniform across the entire flow domain, I show theoretically that the Gaussian closure method could apply to spatially variable a statistics.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectSTOCHASTICen_US
dc.subjectUNSATURATED FLOWen_US
dc.subjectHETEROGENEOUS SOILSen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineHydrologyen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNeuman, Shlomo P.en_US
dc.contributor.chairNeuman, Shlomo P.en_US
dc.contributor.committeememberMaddock, III, Thomasen_US
dc.contributor.committeememberMyers, Donald E.en_US
dc.contributor.committeememberTartakovsky, Danielen_US
dc.identifier.proquest1331en_US
dc.identifier.oclc137355064en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.