{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115642"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115642","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An augmented basis method for reduced order models of turbulent flow","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_has_math":false,"creators":["Kaneko, Kento"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical & Applied Mechans","degree_department":null,"school":null,"contributors":["Fischer, Paul","Pearlstein, Arne","Matalon, Moshe","Olson, Luke"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:54Z","subjects":["Reduced Order Model","Model-Order Reduction","Turbulence"],"languages":["en","eng"],"rights":["Copyright 2022 Kento Kaneko"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115642","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fischer, Paul","Pearlstein, Arne","Matalon, Moshe","Olson, Luke"]},{"key":"dc:creator","label":"Author","values":["Kaneko, Kento"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-21"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical & Applied Mechans"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Reduced Order Model","Model-Order Reduction","Turbulence"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Kento Kaneko"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115642"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Kento Kaneko, accepted the attached license on 2022-04-20 at 13:00.","The student, Kento Kaneko, submitted this Dissertation for approval on 2022-04-20 at 13:08.","This Dissertation was approved for publication on 2022-04-21 at 10:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17845 on 2022-11-14 at 00:24:49","Reduced-order models (ROMs) offer a promising approach for parametric analysis of engineering fluid dynamics applications. The standard procedure consists of using solution snapshots to produce a truncated POD basis, which is in turn used in a Galerkin projection of the governing Navier-Stokes equations (NSE). Unfortunately, the standard POD approach has well-known limitations for high Reynolds number flows that are largely attributable to the lack of fine-scale structure in the low-rank POD bases, which tend to be spatially smooth and therefore unable to generate sufficient small-scale dissipation to stabilize the solution for a small number of modes, N. Even with stabilization, the required value of N is often sufficiently large that these approaches are impaired by the O(N3) costs associated with evaluation of the third-order advection tensor at each step of the ROM time-advancement. We present a novel non-intrusive stabilization technique in the form of basis augmentation that, in many cases, reduces the total number of modes required to produce a stable and accurate ROM reconstruction for turbulent flows at modest Reynolds numbers. The approach involves augmenting the standard POD modes with divergence-free projections of subsets of POD-expanded terms originating from the advection term. Differing combinations of these basis elements are considered. Bases that include interactions with lifting function and self-interactions have proven to be quite effective for several challenging flow problems with relatively low values of Nˆ, where Nˆ is the total number of basis including the augmentation modes. We demonstrate this proposed basis set on several challenging problems and compare its stability properties with alternative stabilization approaches for POD-based ROMs."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An augmented basis method for reduced order models of turbulent flow"]}]}],"canonical_facts":{"dc:contributor":["Fischer, Paul","Pearlstein, Arne","Matalon, Moshe","Olson, Luke"],"dc:creator":["Kaneko, Kento"],"dc:date":["2022-05","2022-04-21"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Kento Kaneko, accepted the attached license on 2022-04-20 at 13:00.","The student, Kento Kaneko, submitted this Dissertation for approval on 2022-04-20 at 13:08.","This Dissertation was approved for publication on 2022-04-21 at 10:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17845 on 2022-11-14 at 00:24:49","Reduced-order models (ROMs) offer a promising approach for parametric analysis of engineering fluid dynamics applications. The standard procedure consists of using solution snapshots to produce a truncated POD basis, which is in turn used in a Galerkin projection of the governing Navier-Stokes equations (NSE). Unfortunately, the standard POD approach has well-known limitations for high Reynolds number flows that are largely attributable to the lack of fine-scale structure in the low-rank POD bases, which tend to be spatially smooth and therefore unable to generate sufficient small-scale dissipation to stabilize the solution for a small number of modes, N. Even with stabilization, the required value of N is often sufficiently large that these approaches are impaired by the O(N3) costs associated with evaluation of the third-order advection tensor at each step of the ROM time-advancement. We present a novel non-intrusive stabilization technique in the form of basis augmentation that, in many cases, reduces the total number of modes required to produce a stable and accurate ROM reconstruction for turbulent flows at modest Reynolds numbers. The approach involves augmenting the standard POD modes with divergence-free projections of subsets of POD-expanded terms originating from the advection term. Differing combinations of these basis elements are considered. Bases that include interactions with lifting function and self-interactions have proven to be quite effective for several challenging flow problems with relatively low values of Nˆ, where Nˆ is the total number of basis including the augmentation modes. We demonstrate this proposed basis set on several challenging problems and compare its stability properties with alternative stabilization approaches for POD-based ROMs."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115642"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Kento Kaneko"],"dc:subject":["Reduced Order Model","Model-Order Reduction","Turbulence"],"dc:title":["An augmented basis method for reduced order models of turbulent flow"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Theoretical & Applied Mechans"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:54Z"}