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dc.contributor.advisorArbogast, Todd James, 1957-en
dc.creatorPool, Jamie Micaylaen
dc.date.accessioned2015-11-17T17:20:06Zen
dc.date.available2015-11-17T17:20:06Zen
dc.date.issued2015-08en
dc.date.submittedAugust 2015en
dc.identifierdoi:10.15781/T2VH1Cen
dc.identifier.urihttp://hdl.handle.net/2152/32535en
dc.descriptiontexten
dc.description.abstractThis dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to solve the nonlinear advection problem in multiple spatial dimensions. The schemes combines the ideas of Lagrangian traceline methods with high order WENO reconstructions to compute the mass that flows into a given cell over a time step. These schemes are important since they have a relaxed CFL constraint, and can be run in parallel. In this thesis we provide two improvements to Eulerian-Lagrangian schemes. To do this an integration based WENO (IWENO) interpolation technique is derived by reconstructing the primitive function and differentiating. This technique gives a high order reconstruction of the mass at an arbitrary point. This WENO scheme is used to solve the linear advection problem. A scheme is derived by backwards tracing of quadrature points located on mesh elements. The mass at these tracepoints is used to compute the mass in the trace region, without resolving its boundary. This process defines a high order quadrature Eulerian-Lagrangian WENO (QEL-WENO) scheme that solves the multi-dimensional problem without the need for a spatial splitting technique. The second improvement is for solving the nonlinear advection problem using an approximate velocity field. The velocity field is used to transport mass in the manner of a standard Eulerian-Lagrangian scheme. Then a flux correction is applied to compute the flow across the tracelines. The contribution is to use a variation of the IWENO technique to reduce the stencil size of this computation. Numerical results are presented demonstrating the capabilities of the scheme. An application to two-phase flow in porous media is provided.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.subjectHyperbolic transporten
dc.subjectSemi-Lagrangianen
dc.subjectFinite volumeen
dc.subjectCharacteristicsen
dc.subjectTracelineen
dc.subjectWENO reconstructionen
dc.subjectCompact stencilen
dc.subjectTwo-phaseen
dc.titleA quadrature Eulerian-Lagrangian WENO scheme for reservoir simulationen
dc.typeThesisen
dc.date.updated2015-11-17T17:20:06Zen
dc.contributor.committeeMemberBalhoff, Matthew Ten
dc.contributor.committeeMemberChen, Thomasen
dc.contributor.committeeMemberGonzalez, Oscaren
dc.contributor.committeeMemberVasseur, Alexis Fen
dc.contributor.committeeMemberWheeler, Mary Fen
dc.description.departmentMathematicsen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
dc.creator.orcid0000-0002-8477-1384en


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