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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