{"id":"https://openalex.org/W1979418319","doi":"https://doi.org/10.1137/11082419x","title":"On Deterministic Approximation of the Boltzmann Equation in a Bounded Domain","display_name":"On Deterministic Approximation of the Boltzmann Equation in a Bounded Domain","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1979418319","doi":"https://doi.org/10.1137/11082419x","mag":"1979418319"},"language":"en","primary_location":{"id":"doi:10.1137/11082419x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082419x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1106.1020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035327429","display_name":"Francis Filbet","orcid":"https://orcid.org/0000-0002-2975-4450"},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I4210125161","display_name":"International Center for Transitional Justice","ror":"https://ror.org/038a3t246","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210125161"]}],"countries":["FR","US"],"is_corresponding":true,"raw_author_name":"Francis Filbet","raw_affiliation_strings":["ICJ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICJ","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I4210125161"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035327429"],"corresponding_institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I4210125161"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08580386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"3","first_page":"792","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9944999814033508,"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":0.988099992275238,"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":0.7113184928894043},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.6974250078201294},{"id":"https://openalex.org/keywords/hagen\u2013poiseuille-equation","display_name":"Hagen\u2013Poiseuille equation","score":0.6166741251945496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5856446027755737},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5700697898864746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49749258160591125},{"id":"https://openalex.org/keywords/specular-reflection","display_name":"Specular reflection","score":0.4732570946216583},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.4700181782245636},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4196319282054901},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4152318239212036},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35890626907348633},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17294353246688843},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.15417665243148804}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7113184928894043},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.6974250078201294},{"id":"https://openalex.org/C175336444","wikidata":"https://www.wikidata.org/wiki/Q869854","display_name":"Hagen\u2013Poiseuille equation","level":3,"score":0.6166741251945496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5856446027755737},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5700697898864746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49749258160591125},{"id":"https://openalex.org/C118381688","wikidata":"https://www.wikidata.org/wiki/Q1079524","display_name":"Specular reflection","level":2,"score":0.4732570946216583},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.4700181782245636},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4196319282054901},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4152318239212036},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35890626907348633},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17294353246688843},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.15417665243148804},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/11082419x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11082419x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1106.1020","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1106.1020","pdf_url":"https://arxiv.org/pdf/1106.1020","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:1979418319","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1106.1020","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.384.9575","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.384.9575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/86/32/01/PDF/paper32.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00598324v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00598324","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2012, 10, pp.792-817. &#x27E8;10.1137/11082419X&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-00863201v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00863201","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1540-3459","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1106.1020","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1106.1020","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1106.1020","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1106.1020","pdf_url":"https://arxiv.org/pdf/1106.1020","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1646421803","https://openalex.org/W1968807612","https://openalex.org/W1978434425","https://openalex.org/W1997251924","https://openalex.org/W1998759078","https://openalex.org/W2015135997","https://openalex.org/W2015465424","https://openalex.org/W2015470839","https://openalex.org/W2031051349","https://openalex.org/W2034624900","https://openalex.org/W2036898921","https://openalex.org/W2037850364","https://openalex.org/W2043953726","https://openalex.org/W2045324877","https://openalex.org/W2051358691","https://openalex.org/W2056518217","https://openalex.org/W2071053994","https://openalex.org/W2080330641","https://openalex.org/W2093321557","https://openalex.org/W2094422642","https://openalex.org/W2109409077","https://openalex.org/W2131943337","https://openalex.org/W2132065774","https://openalex.org/W2162483424","https://openalex.org/W2334374518"],"related_works":["https://openalex.org/W2963529535","https://openalex.org/W2100061420","https://openalex.org/W2087360755","https://openalex.org/W2053423645","https://openalex.org/W2357247692","https://openalex.org/W2919468587","https://openalex.org/W2591009766","https://openalex.org/W2374540343","https://openalex.org/W2033006199","https://openalex.org/W2352606587","https://openalex.org/W144922156","https://openalex.org/W1988025684","https://openalex.org/W3206518711","https://openalex.org/W2048948096","https://openalex.org/W1995243016","https://openalex.org/W2040924666","https://openalex.org/W3153360103","https://openalex.org/W3036053350","https://openalex.org/W2963267229","https://openalex.org/W89459163"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"several":[5],"numerical":[6,122,138],"results":[7,123],"performed":[8],"with":[9,61,95],"a":[10,24,48,62,96,105,141],"fully":[11],"deterministic":[12],"scheme":[13,101],"to":[14,110,152,158],"discretize":[15],"the":[16,52,70,82,88,126,131,150,153,159],"Boltzmann":[17,154],"equation":[18,155],"of":[19,51,65,72,74,84,87,136,144],"rarefied":[20,113],"gas":[21],"dynamics":[22],"in":[23,59,76,102,147],"bounded":[25],"domain":[26],"for":[27,112,163],"multiscale":[28],"problems.":[29],"Periodic,":[30],"specular":[31],"reflection":[32],"and":[33,39,79,104,162],"diffusive":[34],"boundary":[35],"conditions":[36],"are":[37],"discussed":[38],"investigated":[40],"numerically.":[41],"The":[42],"collision":[43,53,89],"operator":[44],"is":[45,69,93,156],"treated":[46],"by":[47],"Fourier":[49],"approximation":[50],"integral,":[54],"which":[55],"guarantees":[56],"spectral":[57],"accuracy":[58,135],"velocity":[60,77],"computational":[63],"cost":[64],"$M\\,N\\,\\log(N)$,":[66],"where":[67],"$N$":[68],"number":[71,83],"degrees":[73],"freedom":[75],"space":[78,103],"$M$":[80],"represents":[81],"discrete":[85],"angles":[86],"kernel.":[90],"This":[91],"algorithm":[92],"coupled":[94],"second":[97],"order":[98],"finite":[99],"volume":[100],"time":[106],"discretization":[107],"allowing":[108],"us":[109],"deal":[111],"regimes":[114],"as":[115,117],"well":[116],"their":[118],"hydrodynamic":[119],"limit.":[120],"Our":[121],"show":[124],"that":[125],"proposed":[127],"approach":[128],"significantly":[129],"improves":[130],"near-wall":[132],"nonstationary":[133],"flow":[134],"standard":[137],"methods":[139],"over":[140],"wide":[142],"range":[143],"Knudsen":[145],"numbers,":[146],"particular":[148],"when":[149],"solution":[151],"close":[157],"local":[160],"equilibrium":[161],"slow":[164],"motion":[165],"flows.":[166]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
