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Parameter Dependent Model Reduction for Complex Fluid Flows

dc.contributor.authorJarvis, Christopher Hunteren
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-04-15T08:00:19Zen
dc.date.available2014-04-15T08:00:19Zen
dc.date.issued2014-04-14en
dc.description.abstractWhen applying optimization techniques to complex physical systems, using very large numerical models for the solution of a system of parameter dependent partial differential equations (PDEs) is usually intractable. Surrogate models are used to provide an approximation to the high fidelity models while being computationally cheaper to evaluate. Typically, for time dependent nonlinear problems a reduced order model is built using a basis obtained through proper orthogonal decomposition (POD) and Galerkin projection of the system dynamics. In this thesis we present theoretical and numerical results for parameter dependent model reduction techniques. The methods are motivated by the need for surrogate models specifically designed for nonlinear parameter dependent systems. We focus on methods in which the projection basis also depends on the parameter through extrapolation and interpolation. Numerical examples involving 1D Burgers' equation, 2D Navier-Stokes equations and 2D Boussinesq equations are presented. For each model problem comparison to traditional POD reduced order models will also be presented.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:2360en
dc.identifier.urihttp://hdl.handle.net/10919/47357en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectModel Reductionen
dc.subjectNonlinear Systemsen
dc.subjectFluid Flowsen
dc.titleParameter Dependent Model Reduction for Complex Fluid Flowsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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