dc.contributor.advisor Arbogast, Todd James, 1957- en dc.creator Pool, Jamie Micayla en dc.date.accessioned 2015-11-17T17:20:06Z en dc.date.available 2015-11-17T17:20:06Z en dc.date.issued 2015-08 en dc.date.submitted August 2015 en dc.identifier doi:10.15781/T2VH1C en dc.identifier.uri http://hdl.handle.net/2152/32535 en dc.description text en dc.description.abstract This 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.mimetype application/pdf en dc.language.iso en en dc.subject Hyperbolic transport en dc.subject Semi-Lagrangian en dc.subject Finite volume en dc.subject Characteristics en dc.subject Traceline en dc.subject WENO reconstruction en dc.subject Compact stencil en dc.subject Two-phase en dc.title A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation en dc.type Thesis en dc.date.updated 2015-11-17T17:20:06Z en dc.contributor.committeeMember Balhoff, Matthew T en dc.contributor.committeeMember Chen, Thomas en dc.contributor.committeeMember Gonzalez, Oscar en dc.contributor.committeeMember Vasseur, Alexis F en dc.contributor.committeeMember Wheeler, Mary F en dc.description.department Mathematics en thesis.degree.department Mathematics en thesis.degree.discipline Mathematics en thesis.degree.grantor The University of Texas at Austin en thesis.degree.level Doctoral en thesis.degree.name Doctor of Philosophy en dc.creator.orcid 0000-0002-8477-1384 en
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