Model Reduction of the Coupled Burgers Equation in Conservation Form

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dc.contributor.authorKramer, Borisen
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberDay, Martin V.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:44:18Zen
dc.date.adate2011-08-30en
dc.date.available2014-03-14T20:44:18Zen
dc.date.issued2011-08-23en
dc.date.rdate2011-08-30en
dc.date.sdate2011-08-26en
dc.description.abstractThis thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several numerical experiments. Based on these results, the Group Finite Element method (GFE) appears to be more stable than the standard Finite Element Method. The design and implementation of controllers heavily relies on rapid solutions to complex models such as the Boussinesq equations. Thus, we further examine the feasibility and efficiency of the Proper Orthogonal Decomposition (POD) for the coupled Burgers equation. Using POD, we reduce the system to a "minimal" number of ODE's and conduct numerous numerical studies comparing the POD and GFE method. Further numerical experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-08262011-115636en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08262011-115636/en
dc.identifier.urihttp://hdl.handle.net/10919/34791en
dc.publisherVirginia Techen
dc.relation.haspartKramer_B_T_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCoupled Burgers Equationen
dc.subjectGroup PODen
dc.subjectFEMen
dc.titleModel Reduction of the Coupled Burgers Equation in Conservation Formen
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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