Virginia Tech
    • Log in
    View Item 
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

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

    Thumbnail
    View/Open
    Hu_WW_D_2012.pdf (4.243Mb)
    Downloads: 13
    Date
    2012-05-21
    Author
    Hu, Weiwei
    Metadata
    Show full item record
    Abstract
    In 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.
    URI
    http://hdl.handle.net/10919/38664
    Collections
    • Doctoral Dissertations [14205]

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us
     

     

    VTechWorks

    AboutPoliciesHelp

    Browse

    All of VTechWorksCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Log inRegister

    Statistics

    View Usage Statistics

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us