Model Reduction of the Coupled Burgers Equation in Conservation Form
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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 â minimalâ number of ODEâ 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.
- Masters Theses