Locally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularity

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dc.contributor.advisorRiviere, Beatrice M.en_US
dc.contributor.committeeMemberHeinkenschloss, Matthiasen_US
dc.contributor.committeeMemberSymes, William W.en_US
dc.contributor.committeeMemberWarburton, Timen_US
dc.creatorLi, Jizhouen_US
dc.date.accessioned2013-09-16T15:48:36Zen_US
dc.date.accessioned2013-09-16T15:48:47Zen_US
dc.date.available2013-09-16T15:48:36Zen_US
dc.date.available2013-09-16T15:48:47Zen_US
dc.date.created2013-05en_US
dc.date.issued2013-09-16en_US
dc.date.submittedMay 2013en_US
dc.date.updated2013-09-16T15:48:47Zen_US
dc.description.abstractThe miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationLi, Jizhou. "Locally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularity." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71985">https://hdl.handle.net/1911/71985</a>.en_US
dc.identifier.slug123456789/ETD-2013-05-539en_US
dc.identifier.urihttps://hdl.handle.net/1911/71985en_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.subjectDiscontinuous Galerkinen_US
dc.subjectMiscible displacementen_US
dc.subjectLow regularityen_US
dc.subjectHigh order time discretizationen_US
dc.subjectMixed finite element methoden_US
dc.subjectStabilityen_US
dc.subjectCompactnessen_US
dc.titleLocally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularityen_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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