A Discontinuous Galerkin Method for Two-phase Flow in Deformable Porous Media

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dc.contributor.advisorRiviere, Beatriceen_US
dc.creatorShen, Boen_US
dc.date.accessioned2020-10-08T19:17:58Zen_US
dc.date.available2020-11-01T05:01:13Zen_US
dc.date.created2020-05en_US
dc.date.issued2020-10-07en_US
dc.date.submittedMay 2020en_US
dc.date.updated2020-10-08T19:17:59Zen_US
dc.description.abstractThe proposed numerical scheme solves the linear poroelasticity equations, which refers to fluid flow within a deformable porous media under the assumption of relative small deformations. More precisely, we approximate the displacement of solid structure, the wetting phase pressure, and saturation of immiscible two-phase fluid flow in the deformable porous media in three dimensions. The model of linear poroelasticity is becoming increasingly essential in a diverse range of engineering fields such as the reservoir, biomedical, and environmental engineering. Thus predicting the deformation of the solid structure and the evolution of the phases in space and time plays an essential role in the risk-managing and decision-making process. The proposed scheme solves the coupled equations sequentially while keeping each equation implicitly with respect to its unknown. A high-order interior penalty discontinuous Galerkin spatial discretization is combined with a backward Euler discretization in time. With this sequential approach, the equations are fully decoupled, which reduces the computational cost significantly compared to the existing implicit approach. Numerical results show the convergence of the scheme with the expected rates.en_US
dc.embargo.terms2020-11-01en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationShen, Bo. "A Discontinuous Galerkin Method for Two-phase Flow in Deformable Porous Media." (2020) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/109397">https://hdl.handle.net/1911/109397</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/109397en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectPoroelasticityen_US
dc.subjectMultiphase flowen_US
dc.subjectcoupled flowen_US
dc.subjectGeomechanicsen_US
dc.subjectNumerical methoden_US
dc.subjectDiscontinuous Galerkin methoden_US
dc.titleA Discontinuous Galerkin Method for Two-phase Flow in Deformable Porous Mediaen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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