{"id":"https://openalex.org/W1989461507","doi":"https://doi.org/10.1137/130908294","title":"Homogenization of High-Contrast Brinkman Flows","display_name":"Homogenization of High-Contrast Brinkman Flows","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1989461507","doi":"https://doi.org/10.1137/130908294","mag":"1989461507"},"language":"en","primary_location":{"id":"doi:10.1137/130908294","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130908294","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086318716","display_name":"Donald L. Brown","orcid":"https://orcid.org/0000-0002-3421-1063"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Donald L. Brown","raw_affiliation_strings":["Institute for Numerical Simulation, University of Bonn, Bonn 53115, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Numerical Simulation, University of Bonn, Bonn 53115, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072051543","display_name":"Yalchin Efendiev","orcid":"https://orcid.org/0000-0001-9626-303X"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Yalchin Efendiev","raw_affiliation_strings":["Center for Numerical Porous Media (NumPor), King Abdullah University of Science and Tech-nology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Numerical Porous Media (NumPor), King Abdullah University of Science and Tech-nology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066860206","display_name":"Guanglian Li","orcid":"https://orcid.org/0000-0003-0615-2681"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guanglian Li","raw_affiliation_strings":["Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M Univer-sity, College Station, TX 77843"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M Univer-sity, College Station, TX 77843","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085364971","display_name":"Viktoria L. Savatorova","orcid":"https://orcid.org/0000-0003-4046-2309"},"institutions":[{"id":"https://openalex.org/I887846188","display_name":"National Research Nuclear University MEPhI","ror":"https://ror.org/04w8z7f34","country_code":"RU","type":"education","lineage":["https://openalex.org/I887846188"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Viktoria Savatorova","raw_affiliation_strings":["Physics Department, N6 NRNU MEPhI, Moscow 115409, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Department, N6 NRNU MEPhI, Moscow 115409, Russia","institution_ids":["https://openalex.org/I887846188"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7058,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73250302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"2","first_page":"472","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9993000030517578,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/homogenization","display_name":"Homogenization (climate)","score":0.9181563854217529},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.5652530193328857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5377601981163025},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5190147161483765},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.4400619864463806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37855154275894165},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2459954023361206},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.2088056206703186},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.18227550387382507},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.13513416051864624}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9181563854217529},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5652530193328857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5377601981163025},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5190147161483765},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.4400619864463806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37855154275894165},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2459954023361206},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.2088056206703186},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.18227550387382507},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.13513416051864624},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/130908294","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130908294","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:pure.rug.nl:openaire_cris_publications/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brown, D L, Efendiev, Y, Li, G & Savatarova, V 2015, 'Homogenization of High Contrast Brinkman flows', Multiscale Modeling & Simulation, vol. 13, no. 2, pp. 472\u2013490. https://doi.org/10.1137/130908294","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:digitalscholarship.unlv.edu:math_fac_articles-1012","is_oa":false,"landing_page_url":"https://digitalscholarship.unlv.edu/math_fac_articles/12","pdf_url":null,"source":{"id":"https://openalex.org/S4377196371","display_name":"Digital Scholarship - UNLV (University of Nevada Reno)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134113660","host_organization_name":"University of Nevada, Reno","host_organization_lineage":["https://openalex.org/I134113660"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Math Faculty Publications","raw_type":"text"},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/179401","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/179401","pdf_url":null,"source":{"id":"https://openalex.org/S4306401674","display_name":"OAKTRUST (Texas A&M University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:oasis.library.unlv.edu:math_fac_articles-1012","is_oa":false,"landing_page_url":"https://oasis.library.unlv.edu/math_fac_articles/12","pdf_url":null,"source":{"id":"https://openalex.org/S4377196371","display_name":"Digital Scholarship - UNLV (University of Nevada Reno)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134113660","host_organization_name":"University of Nevada, Reno","host_organization_lineage":["https://openalex.org/I134113660"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Sciences Faculty Research","raw_type":"article"},{"id":"pmh:oai:pure.rug.nl:openaire/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"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":"Brown, D L, Efendiev, Y, Li, G & Savatarova, V 2015, 'Homogenization of High Contrast Brinkman flows', Multiscale Modeling & Simulation, vol. 13, no. 2, pp. 472\u2013490. https://doi.org/10.1137/130908294","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/592635","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/592635","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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":{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/09bd2c6a-0dfc-44f7-9897-0d856d7946bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brown, D L, Efendiev, Y, Li, G & Savatarova, V 2015, 'Homogenization of High Contrast Brinkman flows', Multiscale Modeling & Simulation, vol. 13, no. 2, pp. 472\u2013490. https://doi.org/10.1137/130908294","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1976873072","https://openalex.org/W1984471539","https://openalex.org/W2027239222","https://openalex.org/W2107589277"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W3101493394","https://openalex.org/W2030735999","https://openalex.org/W2093308788","https://openalex.org/W14390757"],"abstract_inverted_index":{"Modeling":[0],"porous":[1],"flow":[2,25,343,354],"in":[3,22,69,78,182,191,305,344],"complex":[4],"media":[5,72],"is":[6,12,41,76,121,177],"a":[7,79,96,167,236,242,285],"challenging":[8],"problem.":[9],"Not":[10],"only":[11],"the":[13,31,38,70,101,111,114,179,192,227,258,280,289,332,339,350],"problem":[14],"inherently":[15],"multiscale":[16],"but,":[17],"due":[18],"to":[19,123,246,267,279,292,324],"high":[20],"contrast":[21,66,119,321,371],"permeability":[23,63],"values,":[24,322],"velocities":[26],"may":[27],"differ":[28],"greatly":[29],"throughout":[30],"medium.":[32],"To":[33],"avoid":[34],"complicated":[35],"interface":[36],"conditions,":[37],"Brinkman":[39,103,180,260],"model":[40],"often":[42],"used":[43],"for":[44,100,274,288,316,367],"such":[45],"flows":[46],"[O.":[47,293],"Iliev,":[48],"R.":[49],"Lazarov,":[50],"and":[51,65,82,108,118,138,144,201,214,251,270,299,307,320,349,370],"J.":[52,159,206],"Willems,":[53],"Multiscale":[54],"Model.":[55],"Simul.,":[56],"9":[57],"(2011),":[58,209],"pp.":[59,164,210,225],"1350--1372].":[60],"Instead":[61],"of":[62,194],"variations":[64],"being":[67,341,352],"contained":[68,77],"geometric":[71],"structure,":[73],"this":[74,86,254],"information":[75],"highly":[80],"varying":[81],"high-contrast":[83,102],"coefficient.":[84],"In":[85,253,358],"work,":[87],"we":[88,94,256,283,314,361],"present":[89],"two":[90,337],"main":[91],"contributions.":[92],"First,":[93],"develop":[95],"novel":[97],"homogenization":[98,130,196,333],"procedure":[99,334],"equations":[104],"by":[105],"constructing":[106],"correctors":[107,269,290],"carefully":[109],"estimating":[110],"residuals.":[112],"Understanding":[113],"relationship":[115],"between":[116],"scales":[117],"values":[120],"critical":[122],"obtaining":[124],"useful":[125],"estimates.":[126,328],"Therefore,":[127],"standard":[128],"convergence-based":[129],"techniques":[131],"[G.":[132],"A.":[133,135,139,215,294,297,300],"Chechkin,":[134],"L.":[136],"Piatniski,":[137],"S.":[140,301],"Shamev,":[141],"Homogenization:":[142],"Methods":[143],"Applications,":[145],"Transl.":[146],"Math.":[147,160],"Monogr.":[148],"234,":[149],"American":[150],"Mathematical":[151,303],"Society,":[152],"Providence,":[153],"RI,":[154],"2007,":[155],"G.":[156,296],"Allaire,":[157],"SIAM":[158],"Anal.,":[161],"23":[162],"(1992),":[163],"1482--1518],":[165],"although":[166],"powerful":[168],"tool,":[169],"are":[170,186],"not":[171],"applicable":[172],"here.":[173],"Our":[174],"second":[175,351],"point":[176],"that":[178,239],"equations,":[181],"certain":[183,232,275],"scaling":[184],"regimes,":[185],"invariant":[187],"under":[188,231],"homogenization.":[189],"Unlike":[190],"case":[193],"Stokes-to-Darcy":[195],"[D.":[197],"Brown,":[198],"P.":[199],"Popov,":[200],"Y.":[202],"Efendiev,":[203],"GEM":[204],"Int.":[205],"Geomath.,":[207],"2":[208],"281--305,":[211],"E.":[212],"Marusic-Paloka":[213],"Mikelic,":[216],"Boll.":[217],"Un.":[218],"Mat.":[219],"Ital.":[220],"A":[221],"(7),":[222],"10":[223],"(1996),":[224],"661--671],":[226],"results":[228],"presented":[229],"here":[230],"velocity":[233,276],"regimes":[234],"yield":[235],"Brinkman-to-Brinkman":[237],"upscaling":[238],"allows":[240],"using":[241],"single":[243],"software":[244],"platform":[245],"compute":[247],"on":[248,336],"both":[249,317,368],"microscales":[250],"macroscales.":[252],"paper,":[255],"discuss":[257],"homogenized":[259],"equations.":[261],"We":[262,329],"derive":[263],"auxiliary":[264],"cell":[265],"problems":[266],"build":[268],"calculate":[271],"effective":[272],"coefficients":[273],"regimes.":[277],"Due":[278],"boundary":[281,286],"effects,":[282],"construct":[284],"correction":[287],"similar":[291],"Oleinik,":[295],"Iosif'yan,":[298],"Shamaev,":[302],"Problems":[304],"Elasticity":[306],"Homogenization,":[308],"Elsevier,":[309],"Amsterdam,":[310],"1992].":[311],"Using":[312],"residuals,":[313],"estimate":[315],"pore-scales,":[318],"$\\varepsilon$,":[319],"$\\delta$,":[323],"obtain":[325],"our":[326,363],"corrector":[327],"then":[330],"implement":[331],"numerically":[335],"media,":[338],"first":[340],"Stokes":[342],"fractures":[345],"with":[346,355],"Darcy-like":[347,353],"inclusions":[348],"Stokesian":[356],"vuggs.":[357],"these":[359],"examples,":[360],"observe":[362],"theoretical":[364],"convergence":[365],"rates":[366],"pore-scales":[369],"values.":[372]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
