{"id":"https://openalex.org/W1981229339","doi":"https://doi.org/10.1137/080712970","title":"An Immersed Interface Method for the Incompressible Navier\u2013Stokes Equations with Discontinuous Viscosity Across the Interface","display_name":"An Immersed Interface Method for the Incompressible Navier\u2013Stokes Equations with Discontinuous Viscosity Across the Interface","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1981229339","doi":"https://doi.org/10.1137/080712970","mag":"1981229339"},"language":"en","primary_location":{"id":"doi:10.1137/080712970","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080712970","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5033040193","display_name":"Zhijun Tan","orcid":"https://orcid.org/0000-0002-0577-326X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhijun Tan","raw_affiliation_strings":["smatz@nus.edu.sg and smaldv@nus.edu.sg#TAB#"],"affiliations":[{"raw_affiliation_string":"smatz@nus.edu.sg and smaldv@nus.edu.sg#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046643170","display_name":"Duc Vinh Le","orcid":"https://orcid.org/0000-0003-4928-9071"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D.V. Le","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010988075","display_name":"Kian Meng Lim","orcid":"https://orcid.org/0000-0003-4311-9223"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K.M. Lim","raw_affiliation_strings":["mpelimkm@nus.edu.sg and mpekbc@nus.edu.sg#TAB#"],"affiliations":[{"raw_affiliation_string":"mpelimkm@nus.edu.sg and mpekbc@nus.edu.sg#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056015724","display_name":"Boo Cheong Khoo","orcid":"https://orcid.org/0000-0003-4710-4598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B.C. Khoo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033040193"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1419,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.86528635,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"1798","last_page":"1819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9998999834060669,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9998999834060669,"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":0.9944000244140625,"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":0.9940000176429749,"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/discretization","display_name":"Discretization","score":0.6631109714508057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.652852475643158},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5423567891120911},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5181397199630737},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4831520915031433},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4799623489379883},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.46579205989837646},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.44808709621429443},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.43548932671546936},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3410634398460388},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.27442866563796997},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23846375942230225},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19484597444534302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1384594738483429}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6631109714508057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652852475643158},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5423567891120911},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5181397199630737},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4831520915031433},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4799623489379883},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.46579205989837646},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.44808709621429443},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.43548932671546936},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3410634398460388},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.27442866563796997},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23846375942230225},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19484597444534302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1384594738483429},{"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/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C2777813233","wikidata":"https://www.wikidata.org/wiki/Q1527816","display_name":"Grating","level":2,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080712970","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080712970","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/51326","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/51326","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","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":27,"referenced_works":["https://openalex.org/W1504855536","https://openalex.org/W1504917373","https://openalex.org/W1971947347","https://openalex.org/W1982396064","https://openalex.org/W2000068428","https://openalex.org/W2002335991","https://openalex.org/W2004347357","https://openalex.org/W2008368201","https://openalex.org/W2024796148","https://openalex.org/W2025567872","https://openalex.org/W2026352675","https://openalex.org/W2036955083","https://openalex.org/W2039263326","https://openalex.org/W2040290486","https://openalex.org/W2057352214","https://openalex.org/W2071423816","https://openalex.org/W2073237947","https://openalex.org/W2081556070","https://openalex.org/W2084131634","https://openalex.org/W2087535883","https://openalex.org/W2088390336","https://openalex.org/W2095006601","https://openalex.org/W2119315866","https://openalex.org/W2141613219","https://openalex.org/W2143678861","https://openalex.org/W2146913860","https://openalex.org/W2153330556"],"related_works":["https://openalex.org/W1596838038","https://openalex.org/W2321308113","https://openalex.org/W1669816071","https://openalex.org/W2516370737","https://openalex.org/W2004168836","https://openalex.org/W2019487448","https://openalex.org/W571866311","https://openalex.org/W1985944800","https://openalex.org/W3011705631","https://openalex.org/W2073744044"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"immersed":[3,62],"interface":[4,17,63,76,81,140,159,173,189],"method":[5,22,87],"for":[6,106,115],"solving":[7],"the":[8,16,26,43,47,51,58,61,74,80,85,89,107,116,120,130,138,143,155,158,162,167,171,178,181,187,219],"incompressible":[9],"Navier\u2013Stokes":[10,198],"equations":[11,199],"with":[12],"discontinuous":[13,108],"viscosity":[14],"across":[15],"and":[18,33,73,110,127,129,174],"singular":[19],"forces.":[20],"The":[21,122,184,197,214],"is":[23,64,190,222],"based":[24],"on":[25,161,202],"augmented":[27,55,75,139],"strategy":[28],"proposed":[29,59],"by":[30,66,84,207],"Li,":[31],"Ito,":[32],"Lai":[34],"[Comput.":[35],"Fluids,":[36],"36":[37],"(2007),":[38],"pp.":[39],"622\u2013635]":[40],"to":[41,137,177],"decouple":[42],"jump":[44,113,182],"conditions":[45],"of":[46,53,69,119,170,186],"fluid":[48,163,179],"variables":[49,77,141],"through":[50,180],"introduction":[52],"two":[54],"variables.":[56],"In":[57,93],"method,":[60],"represented":[65],"a":[67,98,111,152,203,208],"number":[68],"Lagrangian":[70],"control":[71],"points,":[72],"applicable":[78],"along":[79],"are":[82,135,146,164,175,200],"solved":[83],"LU":[86],"or":[88],"GMRES":[90],"iterative":[91],"method.":[92,213],"addition,":[94],"we":[95],"also":[96],"derive":[97],"new":[99,112],"second":[100,209,223],"order":[101,210,224],"accurate":[102,211],"bilinear":[103],"interpolating":[104],"scheme":[105,221],"velocity":[109,128],"condition":[114],"normal":[117],"derivative":[118],"pressure.":[121],"jumps":[123,131],"in":[124,132],"both":[125],"pressure":[126],"their":[133],"derivatives":[134],"related":[136],"and/or":[142],"forces":[144,156],"which":[145],"interpolated":[147],"using":[148],"cubic":[149],"splines.":[150],"For":[151],"flexible":[153,172,188],"interface,":[154],"that":[157,218],"exerts":[160],"computed":[165],"from":[166],"constitutive":[168],"relation":[169],"applied":[176],"conditions.":[183],"position":[185],"updated":[191],"implicitly":[192],"within":[193],"each":[194],"time":[195],"step.":[196],"discretized":[201],"staggered":[204],"Cartesian":[205],"grid":[206],"projection":[212],"numerical":[215],"results":[216],"show":[217],"overall":[220],"accurate.":[225]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2025-10-10T00:00:00"}