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dc.contributor.advisorArbogast, Todd James, 1957-en
dc.creatorLehr, Heather Lynen
dc.date.accessioned2008-08-28T21:52:18Zen
dc.date.available2008-08-28T21:52:18Zen
dc.date.issued2004en
dc.identifierb59041675en
dc.identifier.urihttp://hdl.handle.net/2152/1234en
dc.descriptiontexten
dc.description.abstractOur goal is to accurately model flow through subsurface systems composed of vuggy porous media. A vug is a small cavity in a porous medium which is large relative to the intergranular pore size. A vuggy porous medium is a porous medium with vugs scattered throughout it. While the vugs are often small, they can have a tremendous effect on the flow of fluid through the medium. We first introduce our microscale mathematical model for flow of an incompressible, viscous fluid in vuggy porous media. Our next step is to obtain a homogenized macroscale model. In order to do so, we assume periodicity of the medium. We obtain necessary existence and uniqueness results, error estimates, and slight generalizations of two-scale convergence results for bi-modal media. First using formal homogenization and then the rigorous two-scale convergence method, we show that our microscale model homogenizes to give a much simpler modified Darcy’s law macroscale model. In this homogenized model, the permeability tensor is modified to capture the effects of the vugs on the flow through the medium. In order to compute the homogenized permeability tensor, we essentially compute our microscale system on a (much smaller) representative cell. Toward this end, we introduce two numerical methods for the microscale model. We combine a discontinuous Galerkin method with a low order RaviartThomas element and obtain suboptimal convergence rates for the first method. The second method differs only slightly from the first, but yields optimal convergence rates. Unfortunately, it is less efficient in practical implementations.
dc.format.mediumelectronicen
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshPorous materials--Mathematical modelsen
dc.subject.lcshFluid dynamics--Mathematical modelsen
dc.subject.lcshDarcy's lawen
dc.subject.lcshStokes equationsen
dc.titleAnalysis of a Darcy-Stokes system modeling flow through vuggy porous mediaen
dc.description.departmentMathematicsen
dc.identifier.oclc57622425en
dc.identifier.proqst3143297en
dc.type.genreThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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