Stabilization of POD-ROMs
dc.contributor.author | Wells, David Reese | en |
dc.contributor.committeechair | Iliescu, Traian | en |
dc.contributor.committeemember | Glatt-Holtz, Nathan | en |
dc.contributor.committeemember | Gugercin, Serkan | en |
dc.contributor.committeemember | Paul, Mark R. | en |
dc.contributor.department | Mathematics | en |
dc.date.accessioned | 2015-06-18T08:01:30Z | en |
dc.date.available | 2015-06-18T08:01:30Z | en |
dc.date.issued | 2015-06-17 | en |
dc.description.abstract | This 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.degree | Ph. D. | en |
dc.format.medium | ETD | en |
dc.identifier.other | vt_gsexam:5371 | en |
dc.identifier.uri | http://hdl.handle.net/10919/52960 | en |
dc.publisher | Virginia Tech | en |
dc.rights | In Copyright | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject | Reduced Order Modeling | en |
dc.subject | Proper Orthogonal Decomposition | en |
dc.subject | Large Eddy Simulation | en |
dc.subject | Regularized Models | en |
dc.subject | Streamline-Upwind Petrov-Galerkin | en |
dc.subject | Scientific Computing | en |
dc.title | Stabilization of POD-ROMs | en |
dc.type | Dissertation | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
thesis.degree.level | doctoral | en |
thesis.degree.name | Ph. D. | en |
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