Title page for ETD etd-08262011-115636

Type of Document Master's Thesis
Author Kramer, Boris
Author's Email Address bokr@vt.edu
URN etd-08262011-115636
Title Model Reduction of the Coupled Burgers Equation in Conservation Form
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Borggaard, Jeffrey T. Committee Member
Day, Martin V. Committee Member
  • Coupled Burgers Equation
  • Group POD
  • FEM
Date of Defense 2011-08-23
Availability unrestricted
This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equa- tion 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 feasibil- ity 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 ex- periments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied.
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