Numerical simulation of one-dimensional and two-dimensional mass transport in groundwater, using Galerkin, Petrov-Galerkin and localized adjoint methods.

Persistent Link:
http://hdl.handle.net/10150/185695
Title:
Numerical simulation of one-dimensional and two-dimensional mass transport in groundwater, using Galerkin, Petrov-Galerkin and localized adjoint methods.
Author:
Souissi, Abderrazak.
Issue Date:
1991
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:
Advection-diffusion transport equations are important in many branches of engineering and applied science. These equations are characterized by a nondissipative (hyperbolic) advective transport component and a dissipative (parabolic) diffusive component. When diffusion is the dominant process, most finite element numerical solution procedures perform well. However, when advection is the dominant transport process, most finite element numerical procedures exhibit some combination of excessive nonphysical oscillations and excessive numerical diffusion. Many numerical methods use Eulerian analysis to solve the advective diffusion equation. Some of them suffer from accuracy limitations, and others suffer from strict Courant number limitation. A Localized Adjoint Petrov-Galerkin Method is proposed to solve the multi-dimensional advection-diffusion equation. The method uses a weight function that is a numerical solution of adjoint state equations on a sequence of nested grids. Solutions corresponding to a given member of the sequence are ideally suited for parallel computation. One-dimensional numerical results are presented. The numerical results demonstrate that the method is accurate for low Peclet numbers. For large Peclet numbers numerical dispersion is introduced in the concentration profiles. Another method, the incomplete cubic Hermitian Galerkin, is presented to solve the transport equation for high Peclet number. One- and two-dimensional numerical results are presented. The numerical results demonstrate less oscillation and dispersion than obtained by linear Galerkin method.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Civil engineering.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Civil Engineering and Engineering Mechanics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Contractor, Dinshaw N.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical simulation of one-dimensional and two-dimensional mass transport in groundwater, using Galerkin, Petrov-Galerkin and localized adjoint methods.en_US
dc.creatorSouissi, Abderrazak.en_US
dc.contributor.authorSouissi, Abderrazak.en_US
dc.date.issued1991en_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.abstractAdvection-diffusion transport equations are important in many branches of engineering and applied science. These equations are characterized by a nondissipative (hyperbolic) advective transport component and a dissipative (parabolic) diffusive component. When diffusion is the dominant process, most finite element numerical solution procedures perform well. However, when advection is the dominant transport process, most finite element numerical procedures exhibit some combination of excessive nonphysical oscillations and excessive numerical diffusion. Many numerical methods use Eulerian analysis to solve the advective diffusion equation. Some of them suffer from accuracy limitations, and others suffer from strict Courant number limitation. A Localized Adjoint Petrov-Galerkin Method is proposed to solve the multi-dimensional advection-diffusion equation. The method uses a weight function that is a numerical solution of adjoint state equations on a sequence of nested grids. Solutions corresponding to a given member of the sequence are ideally suited for parallel computation. One-dimensional numerical results are presented. The numerical results demonstrate that the method is accurate for low Peclet numbers. For large Peclet numbers numerical dispersion is introduced in the concentration profiles. Another method, the incomplete cubic Hermitian Galerkin, is presented to solve the transport equation for high Peclet number. One- and two-dimensional numerical results are presented. The numerical results demonstrate less oscillation and dispersion than obtained by linear Galerkin method.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectCivil engineering.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineCivil Engineering and Engineering Mechanicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorContractor, Dinshaw N.en_US
dc.contributor.committeememberKiousis, Panos D.en_US
dc.contributor.committeememberLansey, Kevin E.en_US
dc.identifier.proquest9210301en_US
dc.identifier.oclc711907099en_US
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