{"id":"https://openalex.org/W1595112045","doi":"https://doi.org/10.1023/a:1021168924020","title":"A Fourth Order Scheme for Incompressible Boussinesq Equations","display_name":"A Fourth Order Scheme for Incompressible Boussinesq Equations","publication_year":2003,"publication_date":"2003-03-21","ids":{"openalex":"https://openalex.org/W1595112045","doi":"https://doi.org/10.1023/a:1021168924020","mag":"1595112045"},"language":"en","primary_location":{"id":"doi:10.1023/a:1021168924020","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1021168924020","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","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/A5019169169","display_name":"Jian\u2010Guo Liu","orcid":"https://orcid.org/0000-0002-9911-4045"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Guo Liu","raw_affiliation_strings":["Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park","Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland\u200920742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland\u200920742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100417045","display_name":"Cheng Wang","orcid":"https://orcid.org/0000-0003-4220-8080"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cheng Wang","raw_affiliation_strings":["Institute for Scientific Computing and Applied Mathematics and Department of Mathematics, Indiana University, Bloomington","Institute for Scientific Computing and Applied Mathematics and Department of Mathematics, Indiana University, Bloomington, Indiana 47405. cwang@indiana.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Scientific Computing and Applied Mathematics and Department of Mathematics, Indiana University, Bloomington","institution_ids":["https://openalex.org/I4210119109"]},{"raw_affiliation_string":"Institute for Scientific Computing and Applied Mathematics and Department of Mathematics, Indiana University, Bloomington, Indiana 47405. cwang@indiana.edu#TAB#","institution_ids":["https://openalex.org/I4210119109"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084920377","display_name":"Hans Johnston","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hans Johnston","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor","Department of Mathematics University of Michigan Ann Arbor, Michigan 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mathematics University of Michigan Ann Arbor, Michigan 48109","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100417045"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.8062,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.69938376,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"253","last_page":"285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9994000196456909,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.759617805480957},{"id":"https://openalex.org/keywords/stencil","display_name":"Stencil","score":0.5773131251335144},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.5361608862876892},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.4930674731731415},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4415304958820343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4409591555595398},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.43199318647384644},{"id":"https://openalex.org/keywords/boussinesq-approximation","display_name":"Boussinesq approximation (buoyancy)","score":0.41917258501052856},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4142667353153229},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.4135294258594513},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.3377745747566223},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.30855658650398254},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.24739709496498108},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23336681723594666},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.15301692485809326},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14607617259025574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.759617805480957},{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.5773131251335144},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.5361608862876892},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.4930674731731415},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4415304958820343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4409591555595398},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.43199318647384644},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.41917258501052856},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4142667353153229},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.4135294258594513},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.3377745747566223},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.30855658650398254},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.24739709496498108},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23336681723594666},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.15301692485809326},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14607617259025574},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.0},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.0},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.0},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1023/a:1021168924020","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1021168924020","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.722.9686","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.722.9686","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.duke.edu/%7Ejliu/research/pdf/Liu_Wang_Johnston_JSC_2003.pdf","raw_type":"text"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/44978","is_oa":false,"landing_page_url":"http://hdl.handle.net/2027.42/44978","pdf_url":null,"source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W67812752","https://openalex.org/W119212728","https://openalex.org/W1521454588","https://openalex.org/W1968373396","https://openalex.org/W1989006912","https://openalex.org/W1996594743","https://openalex.org/W2013546773","https://openalex.org/W2017258831","https://openalex.org/W2029545474","https://openalex.org/W2033462597","https://openalex.org/W2036138588","https://openalex.org/W2060180904","https://openalex.org/W2061170279","https://openalex.org/W2074520269","https://openalex.org/W2106877204","https://openalex.org/W2114972463","https://openalex.org/W2143234699","https://openalex.org/W2163802086","https://openalex.org/W2166590326","https://openalex.org/W2481931709","https://openalex.org/W2489301164","https://openalex.org/W3011214004"],"related_works":["https://openalex.org/W2016023133","https://openalex.org/W2152834265","https://openalex.org/W1616492174","https://openalex.org/W2521969096","https://openalex.org/W1578404675","https://openalex.org/W2027253376","https://openalex.org/W1973178145","https://openalex.org/W1996259749","https://openalex.org/W4406217407","https://openalex.org/W2386606766"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
