{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/115058"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/115058","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations","abstract":"In 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.","abstract_html":"In 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. 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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."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["In 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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Iliescu, Traian"],"dc:contributor.committeemember":["Liu, Honghu","Sun, Shu Ming"],"dc:contributor.department":["Mathematics"],"dc:creator":["Park, Dylan"],"dc:date.accessioned":["2023-05-16T08:01:08Z"],"dc:date.available":["2023-05-16T08:01:08Z"],"dc:date.issued":["2023-05-15"],"dc:description.abstract":["In 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. 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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. 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