Stabilization of POD-ROMs

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.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.publisherVirginia Techen
dc.rightsIn Copyrighten
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 Polytechnic Institute and State Universityen D.en


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