Reduced Order Model Study of Burgers' Equation using Proper Orthogonal Decomposition

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dc.contributor.authorJarvis, Christopher Hunteren
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:32:59Zen
dc.date.adate2012-05-08en
dc.date.available2014-03-14T20:32:59Zen
dc.date.issued2012-02-21en
dc.date.rdate2012-05-08en
dc.date.sdate2012-03-30en
dc.description.abstractIn this thesis we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for selection of optimal parameter values in a trade space and second, identify impacts from changes of parameter values that occur during development, production and sustainment of the designs. To facilitate this study we apply a Finite Element Method (FEM) and where applicable, the Group Finite Element Method (GFE) due its demonstrated stability and reduced complexity over the standard FEM. We also utilize Proper Orthogonal Decomposition (POD) as a model reduction technique and modifications of POD that include Global POD, and the sensitivity based modifications Extrapolated POD and Expanded POD. We then use a single baseline parameter in the parameter range to develop a ROM basis for each method above and investigate the error of each ROM method against a full order "truth" solution for the full parameter range.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-03302012-140735en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03302012-140735/en
dc.identifier.urihttp://hdl.handle.net/10919/31580en
dc.publisherVirginia Techen
dc.relation.haspartJarvis_CH_T_2012.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectReduced Order Modelen
dc.subjectProper Orthogonal Decompositionen
dc.subjectSensitivityen
dc.titleReduced Order Model Study of Burgers' Equation using Proper Orthogonal Decompositionen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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