A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations

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dc.contributor.authorPark, Dylanen
dc.contributor.committeechairIliescu, Traianen
dc.contributor.committeememberLiu, Honghuen
dc.contributor.committeememberSun, Shu Mingen
dc.contributor.departmentMathematicsen
dc.date.accessioned2023-05-16T08:01:08Zen
dc.date.available2023-05-16T08:01:08Zen
dc.date.issued2023-05-15en
dc.description.abstractIn this thesis we propose, analyze, and investigate numerically a novel two-level Galerkin reduced order model (2L-ROM) for the efficient and accurate numerical simulation of the steady Navier-Stokes equations. In the first step of the 2L-ROM, a relatively low-dimensional nonlinear system is solved. In the second step, the Navier-Stokes equations are linearized around the solution found in the first step, and a higher-dimensional system for the linearized problem is solved. We prove an error bound for the new 2L-ROM and compare it to the standard Galerkin ROM, or one-level ROM (1L-ROM), in the numerical simulation of the steady Burgers equation. The 2L-ROM significantly decreases (by a factor of 2 and even 3) the 1L-ROM computational cost, without compromising its numerical accuracy.en
dc.description.abstractgeneralIn this thesis we introduce a new method for efficiently and accurately simulating fluid flow, the Navier-Stokes equations, called the two-level Galerkin reduced order model (2L-ROM). The 2L-ROM involves solving a relatively low-dimensional nonlinear system in the first step, followed by a higher-dimensional linearized system in the second step. We show that this method produces highly accurate results while significantly reducing computational costs compared to previous methods. We provide a comparison between the 2L-ROM and the standard Galerkin ROM, or one-level ROM (1L-ROM), by modeling the steady Burgers equation, as an example. Our results demonstrate that the 2L-ROM reduces the computational cost of the 1L-ROM by a factor of 2 to 3 without sacrificing accuracy.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:36715en
dc.identifier.urihttp://hdl.handle.net/10919/115058en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectReduced Order Modelingen
dc.subjectTwo-Levelen
dc.subjectNumerical Analysisen
dc.subjectScientific Computingen
dc.titleA Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equationsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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