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dc.contributor.advisorEfendiev, Yalchin
dc.creatorDostert, Paul Francis
dc.date.accessioned2010-01-15T00:07:00Z
dc.date.accessioned2010-01-16T00:39:22Z
dc.date.available2010-01-15T00:07:00Z
dc.date.available2010-01-16T00:39:22Z
dc.date.created2007-12
dc.date.issued2009-05-15
dc.identifier.urihttps://hdl.handle.net/1969.1/ETD-TAMU-2532
dc.description.abstractIn this dissertation we discuss numerical methods used for uncertainty quantifi- cation applications to flow in porous media. We consider stochastic flow equations that contain both a spatial and random component which must be resolved in our numerical models. When solving the flow and transport through heterogeneous porous media some type of upscaling or coarsening is needed due to scale disparity. We describe multiscale techniques used for solving the spatial component of the stochastic flow equations. These techniques allow us to simulate the flow and transport processes on the coarse grid and thus reduce the computational cost. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically, polynomial chaos methods and sparse grid collocation methods. We apply the proposed methods to uncertainty quantification problems where the goal is to sample porous media properties given an integrated response. We propose several efficient sampling algorithms based on Langevin diffusion and the Markov chain Monte Carlo method. Analysis and detailed numerical results are presented for applications in multiscale immiscible flow and water infiltration into a porous medium.en
dc.format.mediumelectronicen
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.subjectUpscalingen
dc.subjectMCMCen
dc.titleUncertainty quantification using multiscale methods for porous media flowsen
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A&M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberDatta-Gupta, Akhil
dc.contributor.committeeMemberEwing, Richard E.
dc.contributor.committeeMemberLazarov, Raytcho
dc.contributor.committeeMemberMallick, Bani
dc.type.genreElectronic Dissertationen
dc.type.materialtexten
dc.format.digitalOriginborn digitalen


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