{"id":"https://openalex.org/W2070945030","doi":"https://doi.org/10.1080/00207160701308309","title":"Radial basis function meshless method for the steady incompressible Navier\u2013Stokes equations","display_name":"Radial basis function meshless method for the steady incompressible Navier\u2013Stokes equations","publication_year":2007,"publication_date":"2007-09-25","ids":{"openalex":"https://openalex.org/W2070945030","doi":"https://doi.org/10.1080/00207160701308309","mag":"2070945030"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701308309","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701308309","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5047904639","display_name":"Phani Chinchapatnam","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Phani P. Chinchapatnam","raw_affiliation_strings":["Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007703598","display_name":"K. Djidjeli","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"K. Djidjeli","raw_affiliation_strings":["Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075671693","display_name":"Prasanth B. Nair","orcid":"https://orcid.org/0000-0001-7371-1223"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Prasanth B. Nair","raw_affiliation_strings":["Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Design Group , University of Southampton , Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Computational Engineering and Design Group, University of Southampton, Southampton, UK#TAB#","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007703598"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":null,"apc_paid":null,"fwci":1.3812,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.82248143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"84","issue":"10","first_page":"1509","last_page":"1521"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12293","display_name":"Dam Engineering and Safety","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/regularized-meshless-method","display_name":"Regularized meshless method","score":0.7991706132888794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7210550904273987},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6047930717468262},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.5798133611679077},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5335918664932251},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5146635174751282},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5057969093322754},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5023899078369141},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4914160966873169},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.49085456132888794},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.485518217086792},{"id":"https://openalex.org/keywords/stream-function","display_name":"Stream function","score":0.4397295117378235},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.43585580587387085},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3818652033805847},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.3170672655105591},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19125893712043762},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16037437319755554},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.14726030826568604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13451525568962097},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1299787163734436},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.12970763444900513},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12235063314437866},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.1024634838104248},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.07887250185012817},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.07801628112792969}],"concepts":[{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.7991706132888794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7210550904273987},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6047930717468262},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.5798133611679077},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5335918664932251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5146635174751282},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5057969093322754},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5023899078369141},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4914160966873169},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.49085456132888794},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.485518217086792},{"id":"https://openalex.org/C18932819","wikidata":"https://www.wikidata.org/wiki/Q2029236","display_name":"Stream function","level":4,"score":0.4397295117378235},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.43585580587387085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3818652033805847},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3170672655105591},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19125893712043762},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16037437319755554},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.14726030826568604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13451525568962097},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1299787163734436},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12970763444900513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12235063314437866},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.1024634838104248},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.07887250185012817},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.07801628112792969},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160701308309","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701308309","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:48783","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/48783/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W156601880","https://openalex.org/W194065154","https://openalex.org/W1503437626","https://openalex.org/W1815731809","https://openalex.org/W1972321468","https://openalex.org/W1974036520","https://openalex.org/W1977027705","https://openalex.org/W1988793248","https://openalex.org/W2001442636","https://openalex.org/W2004015934","https://openalex.org/W2008380267","https://openalex.org/W2015725973","https://openalex.org/W2021041911","https://openalex.org/W2041858377","https://openalex.org/W2046230872","https://openalex.org/W2047877145","https://openalex.org/W2048083004","https://openalex.org/W2048680633","https://openalex.org/W2054732436","https://openalex.org/W2055528045","https://openalex.org/W2057667075","https://openalex.org/W2070525652","https://openalex.org/W2070616380","https://openalex.org/W2071467620","https://openalex.org/W2074402890","https://openalex.org/W2079929209","https://openalex.org/W2080977367","https://openalex.org/W2082023789","https://openalex.org/W2092011174","https://openalex.org/W2101549701","https://openalex.org/W2142136198","https://openalex.org/W2145364658","https://openalex.org/W2801083311","https://openalex.org/W3114150879","https://openalex.org/W3134365925","https://openalex.org/W4238065479","https://openalex.org/W6606371587","https://openalex.org/W6791003582"],"related_works":["https://openalex.org/W2089665536","https://openalex.org/W2357878399","https://openalex.org/W2045244898","https://openalex.org/W3103817515","https://openalex.org/W32014465","https://openalex.org/W2585431206","https://openalex.org/W2013931185","https://openalex.org/W2066873213","https://openalex.org/W3011054991","https://openalex.org/W2070945030"],"abstract_inverted_index":{"A":[0],"meshless":[1],"collocation":[2],"method":[3,19,42,63],"based":[4],"on":[5],"radial":[6],"basis":[7],"functions":[8],"is":[9,64],"proposed":[10],"for":[11,43],"solving":[12,24,44,67],"the":[13,21,25,32,36,45,71],"steady":[14],"incompressible":[15],"Navier\u2013Stokes":[16],"equations.":[17],"This":[18],"has":[20],"capability":[22],"of":[23,61],"governing":[26],"equations":[27],"using":[28,54],"scattered":[29],"nodes":[30],"in":[31,75,90],"domain.":[33],"We":[34],"use":[35],"streamfunction":[37],"formulation,":[38],"and":[39,77,80],"a":[40,55,83],"trust-region":[41],"nonlinear":[46],"problem.":[47],"The":[48,59,86],"no-slip":[49],"boundary":[50],"conditions":[51],"are":[52,89],"satisfied":[53],"ghost":[56],"node":[57],"strategy.":[58],"efficiency":[60],"this":[62],"demonstrated":[65],"by":[66],"three":[68],"model":[69],"problems:":[70],"driven":[72],"cavity":[73],"flows":[74],"square":[76],"rectangular":[78],"domains":[79],"flow":[81],"over":[82],"backward-facing":[84],"step.":[85],"results":[87],"obtained":[88],"good":[91],"agreement":[92],"with":[93],"benchmark":[94],"solutions.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
