Title page for ETD etd-06192012-174604


Type of Document Dissertation
Author Hu, Weiwei
Author's Email Address huweiwei@vt.edu
URN etd-06192012-174604
Title Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Ball, Joseph A. Committee Member
Borggaard, Jeffrey T. Committee Member
Cliff, Eugene M. Committee Member
Zietsman, Lizette Committee Member
Keywords
  • Taylor-Hood Elements
  • Analytic Semigroup
  • Algebraic Riccati Equation
  • LQR Control
  • Boundary Feedback Control
  • Boussinesq Equations
Date of Defense 2012-05-21
Availability restricted
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.
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