{"id":"https://openalex.org/W2475859301","doi":"https://doi.org/10.1142/s0218127416500863","title":"Numerical Investigation of the \u201cPoor Man\u2019s Navier\u2013Stokes Equations\u201d with Darcy and Forchheimer Terms","display_name":"Numerical Investigation of the \u201cPoor Man\u2019s Navier\u2013Stokes Equations\u201d with Darcy and Forchheimer Terms","publication_year":2016,"publication_date":"2016-05-01","ids":{"openalex":"https://openalex.org/W2475859301","doi":"https://doi.org/10.1142/s0218127416500863","mag":"2475859301"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500863","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500863","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5101682103","display_name":"Tingting Tang","orcid":"https://orcid.org/0000-0003-2022-9884"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tingting Tang","raw_affiliation_strings":["Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100396747","display_name":"Zhiyong Li","orcid":"https://orcid.org/0000-0003-4763-2139"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiyong Li","raw_affiliation_strings":["Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090165175","display_name":"J. M. McDonough","orcid":"https://orcid.org/0000-0001-7493-9502"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. M. McDonough","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA","Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA","institution_ids":["https://openalex.org/I143302722"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506, USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057592767","display_name":"Peter D. Hislop","orcid":"https://orcid.org/0000-0003-3693-0667"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. D. Hislop","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, USA","institution_ids":["https://openalex.org/I143302722"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I143302722"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06275139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"05","first_page":"1650086","last_page":"1650086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9998000264167786,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11371","display_name":"Wind and Air Flow Studies","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5979726910591125},{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.5896840691566467},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.5880694389343262},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5273281931877136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.514225959777832},{"id":"https://openalex.org/keywords/drag","display_name":"Drag","score":0.5025122165679932},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.49868178367614746},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.48056796193122864},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4796034097671509},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4560839831829071},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43024390935897827},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.4116075932979584},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3880401849746704},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3689766526222229},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33366626501083374},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.12413585186004639},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.08341014385223389}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5979726910591125},{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.5896840691566467},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5880694389343262},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5273281931877136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.514225959777832},{"id":"https://openalex.org/C72921944","wikidata":"https://www.wikidata.org/wiki/Q206621","display_name":"Drag","level":2,"score":0.5025122165679932},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.49868178367614746},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.48056796193122864},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4796034097671509},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4560839831829071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43024390935897827},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.4116075932979584},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3880401849746704},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3689766526222229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33366626501083374},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.12413585186004639},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.08341014385223389},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500863","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500863","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","display_name":"No poverty","score":0.7599999904632568}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309825","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W143911530","https://openalex.org/W182197316","https://openalex.org/W1601140385","https://openalex.org/W1988847099","https://openalex.org/W1989091039","https://openalex.org/W1992209826","https://openalex.org/W1993389546","https://openalex.org/W2012206558","https://openalex.org/W2039855718","https://openalex.org/W2042403115","https://openalex.org/W2048744043","https://openalex.org/W2051666332","https://openalex.org/W2064845881","https://openalex.org/W2080766157","https://openalex.org/W2102892532","https://openalex.org/W2124189636","https://openalex.org/W2144690731","https://openalex.org/W2149674609","https://openalex.org/W2152608122","https://openalex.org/W2163831147","https://openalex.org/W2168711358","https://openalex.org/W2462047076","https://openalex.org/W3025560754","https://openalex.org/W4234284487","https://openalex.org/W4243066586"],"related_works":["https://openalex.org/W2339458745","https://openalex.org/W2009968757","https://openalex.org/W3014342693","https://openalex.org/W2561007490","https://openalex.org/W4386041468","https://openalex.org/W1908764089","https://openalex.org/W3107946728","https://openalex.org/W2997277497","https://openalex.org/W3171752347","https://openalex.org/W2888482338"],"abstract_inverted_index":{"In":[0],"this":[1,109],"paper,":[2],"a":[3,22],"discrete":[4],"dynamical":[5],"system":[6,91],"(DDS)":[7],"is":[8,36,71],"derived":[9],"from":[10,28,105],"the":[11,29,37,50,63,74,106],"generalized":[12],"Navier\u2013Stokes":[13,34],"equations":[14,35],"for":[15,43,120],"incompressible":[16],"flow":[17,99,125],"in":[18,73,93,114],"porous":[19,101,127],"media":[20],"via":[21],"Galerkin":[23],"procedure.":[24],"The":[25],"main":[26],"difference":[27],"previously":[30],"studied":[31],"poor":[32],"man\u2019s":[33],"addition":[38],"of":[39,49,76,87,117,123],"forcing":[40],"terms":[41,70],"accounting":[42],"linear":[44],"and":[45,54,85],"nonlinear":[46],"drag":[47],"forces":[48],"medium":[51],"\u2014":[52],"Darcy":[53],"Forchheimer":[55],"terms.":[56],"A":[57],"detailed":[58],"numerical":[59],"investigation":[60],"focusing":[61],"on":[62],"bifurcation":[64],"parameters":[65],"due":[66],"to":[67],"these":[68],"additional":[69],"provided":[72],"form":[75,119],"regime":[77],"maps,":[78],"time":[79],"series,":[80],"power":[81],"spectra,":[82],"phase":[83],"portraits":[84],"basins":[86],"attraction,":[88],"which":[89],"indicate":[90],"behaviors":[92],"agreement":[94],"with":[95],"expected":[96],"physical":[97],"fluid":[98],"through":[100,126],"media.":[102,128],"As":[103],"concluded":[104],"previous":[107],"studies,":[108],"DDS":[110],"can":[111],"be":[112],"employed":[113],"subgrid-scale":[115],"models":[116],"synthetic-velocity":[118],"large-eddy":[121],"simulation":[122],"turbulent":[124]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
