{"id":"https://openalex.org/W4407001070","doi":"https://doi.org/10.1007/s11075-025-02013-z","title":"Optimal Control problems of NS-$$\\alpha $$ and NS-$$\\omega $$ turbulence models: analysis and numerical tests","display_name":"Optimal Control problems of NS-$$\\alpha $$ and NS-$$\\omega $$ turbulence models: analysis and numerical tests","publication_year":2025,"publication_date":"2025-01-30","ids":{"openalex":"https://openalex.org/W4407001070","doi":"https://doi.org/10.1007/s11075-025-02013-z"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-025-02013-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02013-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02013-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02013-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012257460","display_name":"G\u00fclnur Ha\u00e7at","orcid":"https://orcid.org/0000-0001-7343-8466"},"institutions":[{"id":"https://openalex.org/I40790370","display_name":"Yalova University","ror":"https://ror.org/01x18ax09","country_code":"TR","type":"education","lineage":["https://openalex.org/I40790370"]},{"id":"https://openalex.org/I95634034","display_name":"Gazi University","ror":"https://ror.org/054xkpr46","country_code":"TR","type":"education","lineage":["https://openalex.org/I95634034"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"G\u00fclnur Ha\u00e7at","raw_affiliation_strings":["Department of Business Administration, Yalova University, 77200, Yalova, Turkey","Graduate School of Natural and Applied Sciences, Gazi University, 06560, Ankara, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Business Administration, Yalova University, 77200, Yalova, Turkey","institution_ids":["https://openalex.org/I40790370"]},{"raw_affiliation_string":"Graduate School of Natural and Applied Sciences, Gazi University, 06560, Ankara, Turkey","institution_ids":["https://openalex.org/I95634034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043988151","display_name":"Aytekin \u00c7\u0131b\u0131k","orcid":"https://orcid.org/0000-0003-3571-4137"},"institutions":[{"id":"https://openalex.org/I95634034","display_name":"Gazi University","ror":"https://ror.org/054xkpr46","country_code":"TR","type":"education","lineage":["https://openalex.org/I95634034"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Aytekin \u00c7\u0131b\u0131k","raw_affiliation_strings":["Department of Mathematics, Gazi University, 06560, Ankara, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gazi University, 06560, Ankara, Turkey","institution_ids":["https://openalex.org/I95634034"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049431096","display_name":"Fikriye Y\u0131lmaz","orcid":null},"institutions":[{"id":"https://openalex.org/I95634034","display_name":"Gazi University","ror":"https://ror.org/054xkpr46","country_code":"TR","type":"education","lineage":["https://openalex.org/I95634034"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Fikriye Y\u0131lmaz","raw_affiliation_strings":["Department of Mathematics, Gazi University, 06560, Ankara, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Gazi University, 06560, Ankara, Turkey","institution_ids":["https://openalex.org/I95634034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046259835","display_name":"Song\u00fcl Kaya","orcid":"https://orcid.org/0000-0003-4231-3630"},"institutions":[{"id":"https://openalex.org/I201799495","display_name":"Middle East Technical University","ror":"https://ror.org/014weej12","country_code":"TR","type":"education","lineage":["https://openalex.org/I201799495"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Song\u00fcl Kaya","raw_affiliation_strings":["Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey","institution_ids":["https://openalex.org/I201799495"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012257460"],"corresponding_institution_ids":["https://openalex.org/I40790370","https://openalex.org/I95634034"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.7875,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.8596816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"101","issue":"1","first_page":"477","last_page":"507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9955999851226807,"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"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9955999851226807,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9940999746322632,"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"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.8421601057052612},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.672890305519104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.663440465927124},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6085504293441772},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5385423898696899},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.5242845416069031},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4504181742668152},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31312453746795654},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23091775178909302},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15957969427108765},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.15020889043807983},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1362043023109436}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.8421601057052612},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.672890305519104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.663440465927124},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6085504293441772},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5385423898696899},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.5242845416069031},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4504181742668152},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31312453746795654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23091775178909302},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15957969427108765},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.15020889043807983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1362043023109436},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"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/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-025-02013-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02013-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02013-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:https://open.metu.edu.tr:11511/113641","is_oa":true,"landing_page_url":"https://hdl.handle.net/11511/113641","pdf_url":"https://open.metu.edu.tr/bitstream/handle/11511/113641/s11075-025-02013-z.pdf","source":{"id":"https://openalex.org/S4306402495","display_name":"OpenMETU (Middle East Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201799495","host_organization_name":"Middle East Technical University","host_organization_lineage":["https://openalex.org/I201799495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s11075-025-02013-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-025-02013-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-025-02013-z.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321861","display_name":"Gazi \u00dcniversitesi","ror":"https://ror.org/054xkpr46"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407001070.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W120623816","https://openalex.org/W1969359215","https://openalex.org/W1972803447","https://openalex.org/W1977135073","https://openalex.org/W1996088437","https://openalex.org/W2001944648","https://openalex.org/W2002230262","https://openalex.org/W2018383942","https://openalex.org/W2029493206","https://openalex.org/W2043660290","https://openalex.org/W2044940921","https://openalex.org/W2063318650","https://openalex.org/W2068044221","https://openalex.org/W2072263829","https://openalex.org/W2074335018","https://openalex.org/W2074377107","https://openalex.org/W2101743932","https://openalex.org/W2106430767","https://openalex.org/W2119471187","https://openalex.org/W2122852406","https://openalex.org/W2292141610","https://openalex.org/W2316889596","https://openalex.org/W2494318439","https://openalex.org/W2545270568","https://openalex.org/W2556472162","https://openalex.org/W3199617915","https://openalex.org/W4280579485","https://openalex.org/W4298228534","https://openalex.org/W4382933070"],"related_works":["https://openalex.org/W4402427056","https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943","https://openalex.org/W2039023896"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,109],"study,":[3],"optimal":[4,82,120],"control":[5,121],"problems":[6],"for":[7,55,61],"the":[8,26,70,73,79,85,89,117,124],"Navier-Stokes-":[9,27],"$$\\alpha":[10,17,91],"$$":[11,18,29,36,92,100],"<mml:math":[12,19,30,37,93,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[13,20,31,38,94,102],"<mml:mi>\u03b1</mml:mi>":[14,21,95],"</mml:math>":[15,22,33,40,96,104],"(NS-":[16,34],")":[23,41],"model":[24,42],"and":[25,49,76,97,128],"$$\\omega":[28,35,99],"<mml:mi>\u03c9</mml:mi>":[32,39,103],"are":[43,47,59,66],"considered.":[44],"Optimality":[45],"conditions":[46],"derived,":[48],"semi-discrete":[50],"a":[51,112],"priori":[52],"error":[53],"estimates":[54],"all":[56],"fluid":[57,107,132],"variables":[58],"analyzed":[60],"both":[62],"models.":[63],"Numerical":[64],"tests":[65],"performed":[67],"to":[68,77,122],"verify":[69],"accuracy":[71],"of":[72,81,88,119,131],"theoretical":[74],"findings":[75],"demonstrate":[78],"effectiveness":[80],"control.":[83],"Given":[84],"proven":[86],"utility":[87],"NS-":[90,98],"models":[105],"in":[106],"dynamics,":[108],"study":[110],"addresses":[111],"significant":[113],"gap":[114],"by":[115],"exploring":[116],"potential":[118],"enhance":[123],"performance,":[125],"efficiency,":[126],"safety,":[127],"environmental":[129],"impact":[130],"systems.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
