{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101093"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101093","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter dependent shocks","abstract":"In this thesis, a new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.","abstract_html":"In this thesis, a new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.","abstract_has_math":false,"creators":["Nair, Nirmal Jayaprasad"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Balajewicz, Maciej"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:32:03Z","date_published":"2018-09-04T20:32:03Z","updated_at":"2026-07-22T22:24:38Z","subjects":["parametric model order reduction","steady state residual","shock","hyperbolic PDE"],"languages":["en"],"rights":["Copyright 2018 by Nirmal Jayaprasad Nair"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101093","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Balajewicz, Maciej"]},{"key":"dc:creator","label":"Author","values":["Nair, Nirmal Jayaprasad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:32:03Z","2018-04-26","2018-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["parametric model order reduction","steady state residual","shock","hyperbolic PDE"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 by Nirmal Jayaprasad Nair"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101093"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, a new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms","The student, Nirmal Jayaprasad Nair, accepted the attached license on 2018-04-26 at 14:00.","The student, Nirmal Jayaprasad Nair, submitted this Thesis for approval on 2018-04-26 at 14:10.","This Thesis was approved for publication on 2018-04-26 at 16:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12526 on 2018-08-31 at 17:15:11","Made available in DSpace on 2018-09-04T20:32:03Z (GMT). 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In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought after parametric reduced-basis arise from solutions of linear transport equations. Key to the proposed approach is the observation that the optimal transport velocities are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-08-31 without embargo terms","The student, Nirmal Jayaprasad Nair, accepted the attached license on 2018-04-26 at 14:00.","The student, Nirmal Jayaprasad Nair, submitted this Thesis for approval on 2018-04-26 at 14:10.","This Thesis was approved for publication on 2018-04-26 at 16:11.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12526 on 2018-08-31 at 17:15:11","Made available in DSpace on 2018-09-04T20:32:03Z (GMT). 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