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Stabilization of POD-ROMs

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dc.contributor.authorWells, David Reeseen
dc.contributor.committeechairIliescu, Traianen
dc.contributor.committeememberGlatt-Holtz, Nathanen
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.committeememberPaul, Mark R.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-06-18T08:01:30Zen
dc.date.available2015-06-18T08:01:30Zen
dc.date.issued2015-06-17en
dc.description.abstractThis thesis describes several approaches for stabilizing POD-ROMs (that is, reduced order models based on basis functions derived from the proper orthogonal decomposition) for both the CDR (convection-diffusion-reaction) equation and the NSEs (Navier-Stokes equations). Stabilization is necessary because standard POD-ROMs of convection-dominated problems usually display numerical instabilities. The first stabilized ROM investigated is a streamline-upwind Petrov-Galerkin ROM (SUPG-ROM). I prove error estimates for the SUPG-ROM and derive optimal scalings for the stabilization parameter. I test the SUPG-ROM with the optimal parameter in the numerical simulation of a convection-dominated CDR problem. The SUPG-ROM yields more accurate results than the standard Galerkin ROM (G-ROM) by eliminating the inherent numerical artifacts (noise) in the data and dampening spurious oscillations. I next propose two regularized ROMs (Reg-ROMs) based on ideas from large eddy simulation and turbulence theory: the Leray ROM (L-ROM) and the evolve-then-filter ROM (EF-ROM). Both Reg-ROMs use explicit POD spatial filtering to regularize (smooth) some of the terms in the standard G-ROM. I propose two different POD spatial filters: one based on the POD projection and a novel POD differential filter. These two new Reg-ROMs and the two spatial filters are investigated in the numerical simulation of the three-dimensional flow past a circular cylinder problem at Re = 100. The numerical results show that EF-ROM-DF is the most accurate Reg-ROM and filter combination and the differential filter generally yields better results than the projection filter. The Reg-ROMs perform significantly better than the standard G-ROM and decrease the CPU time (compared against the direct numerical simulation) by orders of magnitude (from about four days to four minutes).en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:5371en
dc.identifier.urihttp://hdl.handle.net/10919/52960en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectReduced Order Modelingen
dc.subjectProper Orthogonal Decompositionen
dc.subjectLarge Eddy Simulationen
dc.subjectRegularized Modelsen
dc.subjectStreamline-Upwind Petrov-Galerkinen
dc.subjectScientific Computingen
dc.titleStabilization of POD-ROMsen
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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