Abstract
dc:description.abstractThis thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation 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 feasibility 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 experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Kramer, Boris
- Chair dc:contributor.committeechair
-
- Burns, John A.
- Committee members dc:contributor.committeemember
-
- Day, Martin V.
- Borggaard, Jeffrey T.
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-08262011-115636
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/34791