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.
dc.contributor.committeeMemberHeinkenschloss, Matthias
dc.contributor.committeeMemberSymes, William W.
dc.contributor.committeeMemberWarburton, Tim
dc.creatorLi, Jizhou
dc.date.accessioned2013-09-16T15:48:36Z
dc.date.accessioned2013-09-16T15:48:47Z
dc.date.available2013-09-16T15:48:36Z
dc.date.available2013-09-16T15:48:47Z
dc.date.created2013-05
dc.date.issued2013-09-16
dc.date.submittedMay 2013
dc.date.updated2013-09-16T15:48:47Z
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.
dc.format.mimetypeapplication/pdf
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>.
dc.identifier.slug123456789/ETD-2013-05-539
dc.identifier.urihttps://hdl.handle.net/1911/71985
dc.language.isoeng
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.
dc.subjectDiscontinuous Galerkin
dc.subjectMiscible displacement
dc.subjectLow regularity
dc.subjectHigh order time discretization
dc.subjectMixed finite element method
dc.subjectStability
dc.subjectCompactness
dc.titleLocally Mass-Conservative Method With Discontinuous Galerkin In Time For Solving Miscible Displacement Equations Under Low Regularity
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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