This thesis presents and evaluates methods for solving the 1D viscous Burgers' partial differential equation with finite difference, finite element, and proper orthogonal decomposition (POD) methods in the context of an optimal control inverse problem. Based on downstream observations, the initial conditions that optimize a lack-of-fit cost functional are reconstructed for a variety of different Reynolds numbers. For moderate Reynolds numbers, our POD method proves to be not only fast and accurate, it also demonstrates a regularizing effect on the inverse problem. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of
Master of Science. / Summer Semester, 2009. / May 20, 2009. / Reduced Order Modeling, Proper Orthogonal Decomposition, Inverse Problem, Partial Differential Equations, pde, Optimization, Optimal Control, Fluid Dynamics, Finite Difference, Finite Element / Includes bibliographical references. / Ionel M. Navon, Professor Directing Thesis; Max Gunzburger, Committee Member; Gordon Erlebacher, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_253838 |
| Contributors | Steward, Jeff (authoraut), Navon, Ionel M. (professor directing thesis), Gunzburger, Max (committee member), Erlebacher, Gordon (committee member), Department of Scientific Computing (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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