{"id":"https://openalex.org/W2076132681","doi":"https://doi.org/10.1137/030600497","title":"Coarse Graining for Upscaling of Flow in Heterogeneous Porous Media","display_name":"Coarse Graining for Upscaling of Flow in Heterogeneous Porous Media","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2076132681","doi":"https://doi.org/10.1137/030600497","mag":"2076132681"},"language":"en","primary_location":{"id":"doi:10.1137/030600497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600497","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109263750","display_name":"Jens Eberhard","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jens Eberhard","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070210019","display_name":"Sabine Attinger","orcid":"https://orcid.org/0000-0002-7798-7080"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabine Attinger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036489735","display_name":"Gabriel Wittum","orcid":"https://orcid.org/0000-0002-6993-5520"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriel Wittum","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109263750"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0346,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.91189827,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2","issue":"2","first_page":"269","last_page":"301"},"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":0.9994999766349792,"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":0.9990000128746033,"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/granularity","display_name":"Granularity","score":0.8522059917449951},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6509293913841248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5833523869514465},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.4628891348838806},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.41414153575897217},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.397625207901001},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32317212224006653},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26174405217170715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19484207034111023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17085182666778564},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.16772910952568054},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06580254435539246}],"concepts":[{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.8522059917449951},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6509293913841248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5833523869514465},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.4628891348838806},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.41414153575897217},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.397625207901001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32317212224006653},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26174405217170715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19484207034111023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17085182666778564},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.16772910952568054},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06580254435539246},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/030600497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600497","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1974210778","https://openalex.org/W1992111513","https://openalex.org/W2000700004","https://openalex.org/W2001093347","https://openalex.org/W2005329035","https://openalex.org/W2007607138","https://openalex.org/W2018184946","https://openalex.org/W2028017286","https://openalex.org/W2029918260","https://openalex.org/W2034117495","https://openalex.org/W2044156210","https://openalex.org/W2062517214","https://openalex.org/W2069326881","https://openalex.org/W2075019892","https://openalex.org/W2093977531","https://openalex.org/W2117474292","https://openalex.org/W2127894166","https://openalex.org/W2145062249","https://openalex.org/W2148651930","https://openalex.org/W2163764371","https://openalex.org/W2168037806","https://openalex.org/W2480154215","https://openalex.org/W4230055019","https://openalex.org/W4230941884","https://openalex.org/W4245596883"],"related_works":["https://openalex.org/W1991083800","https://openalex.org/W2806984643","https://openalex.org/W4302576814","https://openalex.org/W2950616293","https://openalex.org/W1655003202","https://openalex.org/W2602807540","https://openalex.org/W1650273975","https://openalex.org/W1538649440","https://openalex.org/W4378501849","https://openalex.org/W4383909117"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,37,69,111],"upscaling":[4,17,108,129,136],"of":[5,30,145],"permeability":[6,23,64,93],"and":[7,33,44,77,86,141],"flow":[8,147],"in":[9,41,83,100],"heterogeneous":[10],"porous":[11],"media.":[12],"We":[13,75,122],"develop":[14,105],"a":[15,26,96,106],"new":[16,125],"method":[18,57,82,126],"which":[19,34,67,114],"considers":[20],"the":[21,70,79,91,119,124,142,146,162],"local":[22],"K(x)":[24],"being":[25],"stationary":[27],"random":[28],"field":[29],"lognormal":[31],"distribution":[32],"is":[35,58],"based":[36,110],"filtering":[38],"procedures":[39],"introduced":[40],"Attinger,":[42],"Eberhard,":[43],"Neuss":[45],"[Comput.":[46],"Vis.":[47],"Sci.,":[48],"5":[49],"(2002),":[50],"pp.":[51],"67--72].":[52],"The":[53],"so-called":[54],"coarse":[55,80,112,164],"graining":[56,81,113,165],"used":[59],"to":[60,117],"obtain":[61],"an":[62],"effective":[63,92],"tensor":[65,94],"$K^{\\text{eff}}(\\lam)$":[66],"depends":[68],"given":[71],"length":[72,152],"scale":[73],"$\\lambda$.":[74],"formulate":[76],"extend":[78],"Fourier":[84,101],"space":[85],"give":[87],"explicit":[88],"results":[89],"for":[90,95,150],"correct":[97],"projector":[98],"$P^\\pm_\\lambda$":[99],"space.":[102],"Furthermore,":[103],"we":[104],"numerical":[107,163],"scheme":[109],"allows":[115],"us":[116],"test":[118],"theoretical":[120],"results.":[121],"compare":[123],"with":[127],"simple":[128],"methods":[130],"such":[131],"as":[132],"arithmetic":[133],"or":[134],"geometric":[135],"by":[137],"evaluating":[138],"fluxes":[139],"$Q_\\lambda$":[140],"solutions":[143],"$u_\\lambda$":[144],"equation":[148],"itself":[149],"varying":[151],"scales":[153],"$1/4":[154],"\\leq":[155,157],"\\lambda/l_0":[156],"16$.":[158],"In":[159],"all":[160],"cases":[161],"proves":[166],"best.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
