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Steward, J. (2009). The Solution of a Burgers' Equation Inverse Problem with Reduced-Order Modeling Proper Orthogonal Decomposition. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-0393
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.
Bibliography Note
Includes bibliographical references.
Advisory Committee
Ionel M. Navon, Professor Directing Thesis; Max Gunzburger, Committee Member; Gordon Erlebacher, Committee Member.
Publisher
Florida State University
Identifier
FSU_migr_etd-0393
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Steward, J. (2009). The Solution of a Burgers' Equation Inverse Problem with Reduced-Order Modeling Proper Orthogonal Decomposition. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-0393