{"id":"https://openalex.org/W3135672879","doi":"https://doi.org/10.1137/19m1306609","title":"Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model","display_name":"Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3135672879","doi":"https://doi.org/10.1137/19m1306609","mag":"3135672879"},"language":"en","primary_location":{"id":"doi:10.1137/19m1306609","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1306609","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 & Simulation","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/A5120315408","display_name":"Vincent Perrier","orcid":"https://orcid.org/0009-0009-9538-2542"},"institutions":[{"id":"https://openalex.org/I144889574","display_name":"Universit\u00e9 de Pau et des Pays de l'Adour","ror":"https://ror.org/01frn9647","country_code":"FR","type":"education","lineage":["https://openalex.org/I144889574"]},{"id":"https://openalex.org/I4210091673","display_name":"Laboratoire de Math\u00e9matiques et de leurs Applications","ror":"https://ror.org/00g669j87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I144889574","https://openalex.org/I4210091673","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vincent Perrier","raw_affiliation_strings":["LMAP - Laboratoire de Math\u00e9matiques et de leurs Applications [Pau] (B\u00e2timent IPRA - Universit\u00e9 de Pau et des Pays de l'Adour Avenue de l'Universit\u00e9 - BP 1155 64013 PAU CEDEX - France)","CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments (Centre Inria Bordeaux Sud-Ouest\r\nLaboratoire de Math\u00e9matiques et de leurs Applications de Pau  - France)"],"affiliations":[{"raw_affiliation_string":"LMAP - Laboratoire de Math\u00e9matiques et de leurs Applications [Pau] (B\u00e2timent IPRA - Universit\u00e9 de Pau et des Pays de l'Adour Avenue de l'Universit\u00e9 - BP 1155 64013 PAU CEDEX - France)","institution_ids":["https://openalex.org/I144889574","https://openalex.org/I4210091673"]},{"raw_affiliation_string":"CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments (Centre Inria Bordeaux Sud-Ouest\r\nLaboratoire de Math\u00e9matiques et de leurs Applications de Pau  - France)","institution_ids":["https://openalex.org/I4210091673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032698044","display_name":"Enrique Guti\u00e9rrez","orcid":"https://orcid.org/0000-0002-0045-7372"},"institutions":[{"id":"https://openalex.org/I4210091673","display_name":"Laboratoire de Math\u00e9matiques et de leurs Applications","ror":"https://ror.org/00g669j87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I144889574","https://openalex.org/I4210091673","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I144889574","display_name":"Universit\u00e9 de Pau et des Pays de l'Adour","ror":"https://ror.org/01frn9647","country_code":"FR","type":"education","lineage":["https://openalex.org/I144889574"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Enrique Guti\u00e9rrez","raw_affiliation_strings":["LMAP - Laboratoire de Math\u00e9matiques et de leurs Applications [Pau] (B\u00e2timent IPRA - Universit\u00e9 de Pau et des Pays de l'Adour Avenue de l'Universit\u00e9 - BP 1155 64013 PAU CEDEX - France)","CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments (Centre Inria Bordeaux Sud-Ouest\r\nLaboratoire de Math\u00e9matiques et de leurs Applications de Pau  - France)"],"affiliations":[{"raw_affiliation_string":"LMAP - Laboratoire de Math\u00e9matiques et de leurs Applications [Pau] (B\u00e2timent IPRA - Universit\u00e9 de Pau et des Pays de l'Adour Avenue de l'Universit\u00e9 - BP 1155 64013 PAU CEDEX - France)","institution_ids":["https://openalex.org/I144889574","https://openalex.org/I4210091673"]},{"raw_affiliation_string":"CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments (Centre Inria Bordeaux Sud-Ouest\r\nLaboratoire de Math\u00e9matiques et de leurs Applications de Pau  - France)","institution_ids":["https://openalex.org/I4210091673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5120315408"],"corresponding_institution_ids":["https://openalex.org/I144889574","https://openalex.org/I4210091673"],"apc_list":null,"apc_paid":null,"fwci":0.7121,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.64256216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"1","first_page":"401","last_page":"439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9962999820709229,"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":0.9962999820709229,"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/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.9911999702453613,"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":0.989300012588501,"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/closure","display_name":"Closure (psychology)","score":0.6436401605606079},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6160075068473816},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6129924654960632},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5951251983642578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5843244194984436},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5772663354873657},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5039803385734558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45758453011512756},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.4450737237930298},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1808907389640808},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07498565316200256}],"concepts":[{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6436401605606079},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6160075068473816},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6129924654960632},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5951251983642578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5843244194984436},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5772663354873657},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5039803385734558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45758453011512756},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.4450737237930298},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1808907389640808},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07498565316200256},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1306609","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1306609","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 & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03209659v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-03209659","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"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":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2021, 19 (1), pp.401-439. ⟨10.1137/19M1306609⟩","raw_type":"Journal articles"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/38929","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/38929","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"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":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320323712","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W164706946","https://openalex.org/W1667165204","https://openalex.org/W1963853965","https://openalex.org/W1964751455","https://openalex.org/W1973006924","https://openalex.org/W1977721817","https://openalex.org/W1979656444","https://openalex.org/W1984175055","https://openalex.org/W1984479651","https://openalex.org/W1991812943","https://openalex.org/W1994958147","https://openalex.org/W2006160835","https://openalex.org/W2008068453","https://openalex.org/W2011363712","https://openalex.org/W2011525140","https://openalex.org/W2016281021","https://openalex.org/W2032410035","https://openalex.org/W2063004219","https://openalex.org/W2075776956","https://openalex.org/W2076678844","https://openalex.org/W2077620382","https://openalex.org/W2077819541","https://openalex.org/W2081433561","https://openalex.org/W2114509411","https://openalex.org/W2120062331","https://openalex.org/W2127502481","https://openalex.org/W2132846702","https://openalex.org/W2172718466","https://openalex.org/W2177324328","https://openalex.org/W2237678154","https://openalex.org/W2524245858","https://openalex.org/W2590652987","https://openalex.org/W2592801722","https://openalex.org/W2949739998","https://openalex.org/W2969231521","https://openalex.org/W2979840114","https://openalex.org/W2989313302","https://openalex.org/W3010010017","https://openalex.org/W3136463145","https://openalex.org/W4250741917"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W315394019","https://openalex.org/W2382521049","https://openalex.org/W2923398117","https://openalex.org/W2144385241","https://openalex.org/W4309585848","https://openalex.org/W2265383332","https://openalex.org/W4328130279","https://openalex.org/W2952692593","https://openalex.org/W4376865054"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,152],"show":[4],"how":[5],"to":[6,27,66,110],"derive":[7],"a":[8,17,56,86],"multiphase":[9],"model":[10],"of":[11,69,89,92,121,128,138,148],"Baer":[12,21],"and":[13,22,39,41,61,102,134],"Nunziato":[14,23],"type":[15],"with":[16,55,85,144,162],"simple":[18,57],"stochastic":[19,58],"model.":[20],"models":[24,112,131],"are":[25,64,114,132,142,160],"known":[26],"be":[28,74,106],"unclosed,":[29],"namely,":[30],"they":[31],"depend":[32],"on":[33],"modeling":[34,136],"parameters,":[35],"as":[36],"interfacial":[37,60,101],"velocity":[38],"pressure,":[40],"relaxation":[42,62,103],"terms,":[43],"whose":[44],"exact":[45],"expression":[46],"is":[47],"still":[48],"an":[49,70],"open":[50],"question.":[51],"We":[52],"prove":[53,153],"that":[54,113,154],"model,":[59],"terms":[63],"equivalent":[65],"the":[67,93,100,139,145,149,163],"evaluation":[68],"integral,":[71],"which":[72],"cannot":[73],"explicitly":[75,107],"computed":[76],"in":[77,80],"general.":[78],"However,":[79],"different":[81,111],"particular":[82],"cases":[83],"matching":[84],"large":[87],"range":[88],"applications":[90],"(topology":[91],"bubbles/droplets,":[94],"or":[95,118],"special":[96],"flow":[97],"regime":[98],"conditions),":[99],"parameters":[104,137],"can":[105],"computed,":[108],"leading":[109],"either":[115],"nonlinear":[116],"versions":[117],"slight":[119],"modifications":[120],"previously":[122,129],"proposed":[123,130],"models.":[124],"The":[125],"validity":[126],"domains":[127],"clarified,":[133],"some":[135],"averaged":[140],"system":[141],"linked":[143],"local":[146],"topology":[147],"flow.":[150],"Last,":[151],"usual":[155],"properties":[156],"like":[157],"entropy":[158],"dissipation":[159],"ensured":[161],"new":[164],"closures":[165],"found.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}