{"id":"https://openalex.org/W4414668176","doi":"https://doi.org/10.1007/s10444-025-10257-5","title":"An iterative projection method for unsteady Navier\u2013Stokes equations with high Reynolds numbers","display_name":"An iterative projection method for unsteady Navier\u2013Stokes equations with high Reynolds numbers","publication_year":2025,"publication_date":"2025-09-30","ids":{"openalex":"https://openalex.org/W4414668176","doi":"https://doi.org/10.1007/s10444-025-10257-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-025-10257-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-025-10257-5","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-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/A5008337899","display_name":"Xiaoming Zheng","orcid":"https://orcid.org/0000-0003-0941-9089"},"institutions":[{"id":"https://openalex.org/I1629065","display_name":"Central Michigan University","ror":"https://ror.org/02xawj266","country_code":"US","type":"education","lineage":["https://openalex.org/I1629065"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaoming Zheng","raw_affiliation_strings":["Department of Mathematics, Central Michigan University, Mount Pleasant, MI, 48858, USA"],"raw_orcid":"https://orcid.org/0000-0003-0941-9089","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Central Michigan University, Mount Pleasant, MI, 48858, USA","institution_ids":["https://openalex.org/I1629065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077633829","display_name":"Kun Zhao","orcid":"https://orcid.org/0000-0002-6022-6226"},"institutions":[{"id":"https://openalex.org/I114832834","display_name":"Tulane University","ror":"https://ror.org/04vmvtb21","country_code":"US","type":"education","lineage":["https://openalex.org/I114832834"]},{"id":"https://openalex.org/I1308199089","display_name":"Harbin University","ror":"https://ror.org/00ey9xa07","country_code":"CN","type":"education","lineage":["https://openalex.org/I1308199089"]},{"id":"https://openalex.org/I151727225","display_name":"Harbin Engineering University","ror":"https://ror.org/03x80pn82","country_code":"CN","type":"education","lineage":["https://openalex.org/I151727225"]},{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Kun Zhao","raw_affiliation_strings":["Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA","School of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA","institution_ids":["https://openalex.org/I114832834"]},{"raw_affiliation_string":"School of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, China","institution_ids":["https://openalex.org/I1308199089","https://openalex.org/I151727225","https://openalex.org/I55022517"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100368783","display_name":"Jiahong Wu","orcid":"https://orcid.org/0000-0001-9496-9709"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiahong Wu","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102873604","display_name":"Weiwei Hu","orcid":"https://orcid.org/0000-0002-4752-0893"},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weiwei Hu","raw_affiliation_strings":["Department of Mathematics, University of Georgia, Athens, GA, 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Georgia, Athens, GA, 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101052788","display_name":"Dapeng Du","orcid":null},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dapeng Du","raw_affiliation_strings":["School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin Province, 130024, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin Province, 130024, P.R. China","institution_ids":["https://openalex.org/I184983240"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5008337899","https://openalex.org/A5100368783"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I1629065"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18659757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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":0.9987999796867371,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.6865000128746033},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6223000288009644},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5687999725341797},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5515000224113464},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.5015000104904175},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4643999934196472},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4514000117778778},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45010000467300415},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.39399999380111694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7799000144004822},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.6865000128746033},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6223000288009644},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5687999725341797},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5515000224113464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5042999982833862},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.5015000104904175},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4643999934196472},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45649999380111694},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.34950000047683716},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.334199994802475},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C161666082","wikidata":"https://www.wikidata.org/wiki/Q14551923","display_name":"Oblique projection","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27140000462532043},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.27129998803138733},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-025-10257-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-025-10257-5","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4649135849","display_name":"Collaborative Research: Effective Numerical Schemes for Fundamental Problems Related to Incompressible Fluids","funder_award_id":"2309747","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4703137729","display_name":null,"funder_award_id":"DMS-2005696 (previously DMS-1813570), DMS-2111486 and DMS-2205117","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G4765031779","display_name":"Stabilizing Phenomenon for Incompressible Fluids","funder_award_id":"2104682","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5212110087","display_name":null,"funder_award_id":"No. 413028","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1977424127","https://openalex.org/W1980440487","https://openalex.org/W1994968461","https://openalex.org/W2000068428","https://openalex.org/W2002425660","https://openalex.org/W2051708601","https://openalex.org/W2051862019","https://openalex.org/W2055857105","https://openalex.org/W2065399919","https://openalex.org/W2067556005","https://openalex.org/W2073256259","https://openalex.org/W2076077791","https://openalex.org/W2096130365","https://openalex.org/W2118922968","https://openalex.org/W2140153041","https://openalex.org/W2141870784","https://openalex.org/W2155005220","https://openalex.org/W2164374667","https://openalex.org/W2345742189","https://openalex.org/W2410416051","https://openalex.org/W2491618087","https://openalex.org/W2531452649","https://openalex.org/W2535353373","https://openalex.org/W2563212924","https://openalex.org/W2783022917","https://openalex.org/W2809911513","https://openalex.org/W3083412230","https://openalex.org/W3106336037","https://openalex.org/W3185579339","https://openalex.org/W3204708751","https://openalex.org/W4387742399"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
