Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems

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dc.contributor.authorHu, Weiweien
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:15:11Zen
dc.date.adate2012-07-16en
dc.date.available2014-03-14T21:15:11Zen
dc.date.issued2012-05-21en
dc.date.rdate2012-07-16en
dc.date.sdate2012-06-19en
dc.description.abstractIn this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.en
dc.description.degreePh. D.en
dc.identifier.otheretd-06192012-174604en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06192012-174604/en
dc.identifier.urihttp://hdl.handle.net/10919/38664en
dc.publisherVirginia Techen
dc.relation.haspartHu_WW_D_2012.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectTaylor-Hood Elementsen
dc.subjectAnalytic Semigroupen
dc.subjectAlgebraic Riccati Equationen
dc.subjectLQR Controlen
dc.subjectBoundary Feedback Controlen
dc.subjectBoussinesq Equationsen
dc.titleApproximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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