{"id":"https://openalex.org/W2046269903","doi":"https://doi.org/10.1109/acc.2013.6580013","title":"Reduced order modeling for fluid flows based on nonlinear balanced truncation","display_name":"Reduced order modeling for fluid flows based on nonlinear balanced truncation","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2046269903","doi":"https://doi.org/10.1109/acc.2013.6580013","mag":"2046269903"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2013.6580013","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580013","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076106442","display_name":"Samir Sahyoun","orcid":null},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samir Sahyoun","raw_affiliation_strings":["Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012002316","display_name":"Jin Dong","orcid":"https://orcid.org/0000-0002-5753-1588"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jin Dong","raw_affiliation_strings":["Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107210257","display_name":"Seddik M. Djouadi","orcid":"https://orcid.org/0000-0003-4925-723X"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Seddik M. Djouadi","raw_affiliation_strings":["Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076106442"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.4989,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66334322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"45","issue":null,"first_page":"1284","last_page":"1289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7339999675750732},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.6940900683403015},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.6660062670707703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6639645099639893},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6482737064361572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5955834984779358},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5498627424240112},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5469338297843933},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.45447972416877747},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.4267883896827698},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.4149169325828552},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.4132010340690613},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3810213804244995},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.28268325328826904},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08265691995620728},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06850770115852356}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7339999675750732},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.6940900683403015},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.6660062670707703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639645099639893},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6482737064361572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5955834984779358},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5498627424240112},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5469338297843933},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.45447972416877747},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.4267883896827698},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.4149169325828552},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4132010340690613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3810213804244995},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.28268325328826904},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08265691995620728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06850770115852356},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2013.6580013","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580013","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W167010620","https://openalex.org/W1551480811","https://openalex.org/W1579236455","https://openalex.org/W1609496979","https://openalex.org/W1970809250","https://openalex.org/W1981905989","https://openalex.org/W1991243721","https://openalex.org/W2007581597","https://openalex.org/W2011464857","https://openalex.org/W2015001891","https://openalex.org/W2015665368","https://openalex.org/W2017745440","https://openalex.org/W2059316647","https://openalex.org/W2062393840","https://openalex.org/W2064733273","https://openalex.org/W2077730310","https://openalex.org/W2090906343","https://openalex.org/W2135957782","https://openalex.org/W2138190945","https://openalex.org/W2140820418","https://openalex.org/W2142086611","https://openalex.org/W2147046190","https://openalex.org/W2154930603","https://openalex.org/W2159808517","https://openalex.org/W2169114134","https://openalex.org/W2321052409","https://openalex.org/W2330666245","https://openalex.org/W2334269637","https://openalex.org/W2592244902","https://openalex.org/W3100312030","https://openalex.org/W4213199372","https://openalex.org/W6653030037"],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W2073959938","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2036329708","https://openalex.org/W2073514592"],"abstract_inverted_index":{"For":[0],"a":[1,26,41],"vast":[2],"variety":[3],"of":[4,48,66,78],"fluid":[5],"flows":[6],"the":[7,12,21,33,49,64,89,94,100],"dynamics":[8],"are":[9,16,108],"governed":[10],"by":[11],"Navier-Stokes":[13],"equations":[14],"which":[15,63],"highly":[17],"nonlinear.":[18],"In":[19,38],"particular,":[20],"corresponding":[22],"Galerkin":[23,50],"models":[24,51],"involve":[25],"quadratic":[27],"type":[28],"nonlinearity.":[29],"The":[30,54],"latter":[31],"incudes":[32],"Burgers'":[34],"equation":[35],"as":[36],"well.":[37],"this":[39],"paper,":[40],"computational":[42],"algorithm":[43],"for":[44],"nonlinear":[45,101],"balanced":[46,95],"truncation":[47],"is":[52,56,84],"proposed.":[53],"method":[55],"based":[57],"on":[58],"Taylor":[59],"series":[60],"expansion":[61],"in":[62],"computation":[65],"successively":[67],"higher":[68,75],"order":[69,76],"terms":[70],"reduces":[71],"to":[72,87,98],"solving":[73],"consecutively":[74],"systems":[77],"linear":[79],"algebraic":[80],"equations.":[81],"This":[82],"procedure":[83],"also":[85],"used":[86],"compute":[88,99],"coordinate":[90,106],"transformation":[91,107],"that":[92],"yields":[93],"system.":[96],"Formulas":[97],"controllability,":[102],"observability":[103],"functions":[104],"and":[105],"derived.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}