{"id":"https://openalex.org/W7214899576","doi":"https://doi.org/10.48550/arxiv.2609.37068","title":"Numerical investigation of a homogenized model with effective interface conditions for Stokes flow through porous membranes","display_name":"Numerical investigation of a homogenized model with effective interface conditions for Stokes flow through porous membranes","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214899576","doi":"https://doi.org/10.48550/arxiv.2609.37068"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37068","pdf_url":"https://arxiv.org/pdf/2609.37068","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082693789","display_name":"Jonas Knoch","orcid":"https://orcid.org/0000-0003-4474-3167","observed_orcids":["https://orcid.org/0000-0003-4474-3167"]},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Knoch, Jonas","raw_affiliation_strings":["Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057121254","display_name":"Pietro Italiano","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"education","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Italiano, Pietro","raw_affiliation_strings":["Institute of Geophysics and Geoinformatics , TU Bergakademie Freiberg , Gustav-Zeuner-Stra\u00dfe 12 , 09599 Freiberg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Geophysics and Geoinformatics , TU Bergakademie Freiberg , Gustav-Zeuner-Stra\u00dfe 12 , 09599 Freiberg , Germany","institution_ids":["https://openalex.org/I61893789"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072887891","display_name":"Markus Gahn","orcid":"https://orcid.org/0000-0002-2216-145X","observed_orcids":["https://orcid.org/0000-0002-2216-145X"]},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gahn, Markus","raw_affiliation_strings":["Department Mathematik , Universit\u00e4t Augsburg , Universit\u00e4tsstra\u00dfe 14 , 86159 Augsburg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Mathematik , Universit\u00e4t Augsburg , Universit\u00e4tsstra\u00dfe 14 , 86159 Augsburg , Germany","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009776182","display_name":"Carsten Gr\u00e4ser","orcid":"https://orcid.org/0000-0003-4855-8655","observed_orcids":["https://orcid.org/0000-0003-4855-8655"]},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gr\u00e4ser, Carsten","raw_affiliation_strings":["Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016648054","display_name":"Maria Neuss\u2010Radu","orcid":"https://orcid.org/0000-0003-1788-5354","observed_orcids":["https://orcid.org/0000-0003-1788-5354"]},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Neuss-Radu, Maria","raw_affiliation_strings":["Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Mathematik , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 11 , 91058 Erlangen , Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.00139999995008111,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.746999979019165},{"id":"https://openalex.org/keywords/porous-membranes","display_name":"porous membranes","score":0.8339999914169312},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.8629999756813049},{"id":"https://openalex.org/keywords/transmission-conditions","display_name":"transmission conditions","score":0.8460000157356262},{"id":"https://openalex.org/keywords/two-scale-method","display_name":"two-scale analysis","score":0.597000002861023},{"id":"https://openalex.org/keywords/cell-problems","display_name":"cell problems","score":0.9570000171661377},{"id":"https://openalex.org/keywords/pore-geometry","display_name":"pore geometry","score":0.8320000171661377},{"id":"https://openalex.org/keywords/porous-thin-films","display_name":"porous thin films","score":0.8790000081062317},{"id":"https://openalex.org/keywords/tangential-velocity","display_name":"tangential velocity","score":0.6539999842643738},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.7350000143051147},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.5490000247955322},{"id":"https://openalex.org/keywords/multiscale-modeling","display_name":"multiscale modeling","score":0.5659999847412109}],"concepts":[{"id":"https://openalex.org/C179428855","wikidata":"https://www.wikidata.org/wiki/Q1069216","display_name":"Microscale chemistry","level":2,"score":0.9253000020980835},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6467000246047974},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.6384999752044678},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6370000243186951},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.6323000192642212},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5454999804496765},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.5403000116348267},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.529699981212616},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5041999816894531},{"id":"https://openalex.org/C2988635477","wikidata":"https://www.wikidata.org/wiki/Q28130211","display_name":"Interface model","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3684000074863434},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.31220000982284546},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C166693061","wikidata":"https://www.wikidata.org/wiki/Q5462119","display_name":"Flow velocity","level":3,"score":0.27219998836517334},{"id":"https://openalex.org/C2776950841","wikidata":"https://www.wikidata.org/wiki/Q5450408","display_name":"Finite thickness","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C131043120","wikidata":"https://www.wikidata.org/wiki/Q1543991","display_name":"Potential flow","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37068","pdf_url":"https://arxiv.org/pdf/2609.37068","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.37068","doi":"https://doi.org/10.48550/arxiv.2609.37068","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37068","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37068","pdf_url":"https://arxiv.org/pdf/2609.37068","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,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5940715425","display_name":"Dynamik und Steuerung superparamagnetischer Nanopartikel in einfachen und verzweigten Gef\u00e4\u00dfen: Simulation & Experiment (DyNano)","funder_award_id":"518492286","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214899576.pdf","grobid_xml":"https://content.openalex.org/works/W7214899576.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2112311198","https://openalex.org/W2147811950","https://openalex.org/W2289855022","https://openalex.org/W2976901220","https://openalex.org/W3014388581","https://openalex.org/W3016784457","https://openalex.org/W4399375100","https://openalex.org/W4405083091","https://openalex.org/W4408078353","https://openalex.org/W4416516312","https://openalex.org/W6929372078","https://openalex.org/W6967070185"],"related_works":["https://openalex.org/W2972486553","https://openalex.org/W2336728181","https://openalex.org/W4410362028","https://openalex.org/W6967070185","https://openalex.org/W3126847162","https://openalex.org/W3036759007","https://openalex.org/W7165549958","https://openalex.org/W2563486054","https://openalex.org/W2061817080","https://openalex.org/W2752384894"],"abstract_inverted_index":{"We":[0,116],"investigate":[1],"numerically":[2],"fluid":[3],"flow":[4],"through":[5],"a":[6,14,56,118],"thin":[7,92],"porous":[8,53,93],"layer,":[9],"which":[10],"is":[11],"modelled":[12],"as":[13,136,138],"lower-dimensional":[15],"interface":[16,87,98,132],"separating":[17],"two":[18],"bulk":[19],"domains.":[20],"At":[21],"this":[22],"interface,":[23],"we":[24,59,75,154],"impose":[25],"effective":[26,64,86,97],"transmission":[27,107],"conditions":[28,108],"involving":[29],"homogenized":[30],"coefficients":[31,41,65],"rigorously":[32],"derived":[33],"via":[34],"two-scale":[35],"methods":[36],"in":[37],"previous":[38],"works.":[39],"These":[40],"are":[42,150],"determined":[43],"by":[44,95],"cell":[45],"problems":[46],"encoding":[47],"the":[48,52,63,68,81,85,91,101,104,113,131,142,156,159,169],"microscale":[49,147],"properties":[50],"of":[51,80,158,168],"layer.":[54],"In":[55],"first":[57],"step,":[58],"analyze":[60],"qualitatively":[61],"how":[62],"depend":[66],"on":[67,72],"pore":[69],"geometry.":[70],"Based":[71],"these":[73],"computations,":[74],"then":[76],"present":[77],"numerical":[78,114],"simulations":[79,167],"macroscopic":[82,160],"models":[83,161],"incorporating":[84],"conditions.":[88],"Although":[89],"replacing":[90],"layer":[94],"an":[96],"substantially":[99],"reduces":[100],"computational":[102],"cost,":[103],"resulting":[105,143],"nonstandard":[106],"pose":[109],"additional":[110],"challenges":[111],"for":[112,141,146],"implementation.":[115],"employ":[117],"Taylor--Hood-type":[119],"mixed":[120],"finite":[121],"element":[122],"discretization":[123],"with":[124,162],"discontinuous":[125],"pressure":[126],"and":[127,133],"tangential":[128],"velocity":[129],"across":[130],"prove":[134],"stability":[135],"well":[137],"error":[139],"estimates":[140],"scheme.":[144],"Finally,":[145],"geometries":[148],"that":[149],"still":[151],"computationally":[152],"resolvable,":[153],"compare":[155],"results":[157],"those":[163],"obtained":[164],"from":[165],"direct":[166],"microscopic":[170],"models.":[171]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
