{"id":"https://openalex.org/W4391405497","doi":"https://doi.org/10.3934/nhm.2024006","title":"Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture","display_name":"Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4391405497","doi":"https://doi.org/10.3934/nhm.2024006"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2024006","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024006","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2024006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112842703","display_name":"M. H\u00f6rl","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Maximilian H\u00f6rl","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101833555","display_name":"Christian Rohde","orcid":"https://orcid.org/0000-0001-9183-5094"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Rohde","raw_affiliation_strings":["Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101833555"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":1.5217,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82461558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"19","issue":"1","first_page":"114","last_page":"156"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/limit","display_name":"Limit (mathematics)","score":0.7236216068267822},{"id":"https://openalex.org/keywords/darcys-law","display_name":"Darcy's law","score":0.6438748836517334},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5712051391601562},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5201095342636108},{"id":"https://openalex.org/keywords/fracture","display_name":"Fracture (geology)","score":0.5168964862823486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4738788306713104},{"id":"https://openalex.org/keywords/aperture","display_name":"Aperture (computer memory)","score":0.43752869963645935},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3669445812702179},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35632723569869995},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27748775482177734},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.2405872344970703},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.22326955199241638},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.1164315938949585},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.07892772555351257}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7236216068267822},{"id":"https://openalex.org/C183447037","wikidata":"https://www.wikidata.org/wiki/Q392416","display_name":"Darcy's law","level":4,"score":0.6438748836517334},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5712051391601562},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5201095342636108},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.5168964862823486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4738788306713104},{"id":"https://openalex.org/C78336883","wikidata":"https://www.wikidata.org/wiki/Q4779385","display_name":"Aperture (computer memory)","level":2,"score":0.43752869963645935},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3669445812702179},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35632723569869995},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27748775482177734},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2405872344970703},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.22326955199241638},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.1164315938949585},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.07892772555351257},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2024006","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024006","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:be3c7e3f84e84e368e0f767b6e2f9967","is_oa":true,"landing_page_url":"https://doaj.org/article/be3c7e3f84e84e368e0f767b6e2f9967","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 19, Iss 1, Pp 114-156 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2024006","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024006","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1608407908","https://openalex.org/W1971973036","https://openalex.org/W1972892940","https://openalex.org/W1983067651","https://openalex.org/W2017048267","https://openalex.org/W2024727132","https://openalex.org/W2077064715","https://openalex.org/W2094293004","https://openalex.org/W2124153009","https://openalex.org/W2239446905","https://openalex.org/W2276853594","https://openalex.org/W2472000623","https://openalex.org/W2488917107","https://openalex.org/W2508844586","https://openalex.org/W2549516606","https://openalex.org/W2550941137","https://openalex.org/W2551936914","https://openalex.org/W2734812188","https://openalex.org/W2898230825","https://openalex.org/W2964076483","https://openalex.org/W2998138432","https://openalex.org/W2999720907","https://openalex.org/W3032927343","https://openalex.org/W3080755743","https://openalex.org/W3136158759","https://openalex.org/W3161846186","https://openalex.org/W3163204219","https://openalex.org/W3181458667","https://openalex.org/W3196290810","https://openalex.org/W3211589079","https://openalex.org/W4214743772","https://openalex.org/W4292024663","https://openalex.org/W4296903422","https://openalex.org/W4308654952","https://openalex.org/W4311269708","https://openalex.org/W4382073537","https://openalex.org/W4383534779","https://openalex.org/W4383822777"],"related_works":["https://openalex.org/W2353396818","https://openalex.org/W2370473919","https://openalex.org/W2390876504","https://openalex.org/W2390496461","https://openalex.org/W2389654532","https://openalex.org/W2896003791","https://openalex.org/W2128951066","https://openalex.org/W2369545560","https://openalex.org/W2355429547","https://openalex.org/W2373218684"],"abstract_inverted_index":{"&lt;abstract&gt;&lt;p&gt;We":[0],"consider":[1],"single-phase":[2],"flow":[3],"in":[4,19,54],"a":[5,28,35,69,85,91],"fractured":[6],"porous":[7],"medium":[8],"governed":[9],"by":[10,81],"Darcy's":[11],"law":[12],"with":[13,64],"spatially":[14],"varying":[15],"hydraulic":[16,52],"conductivity":[17],"matrices":[18],"both":[20],"bulk":[21,58],"and":[22,41,57],"fractures.":[23],"The":[24,76],"width-to-length":[25],"ratio":[26,43],"of":[27,31,34,49,87,108],"fracture":[29,56,77],"is":[30,60,79],"the":[32,42,50,55,95,106],"order":[33],"small":[36],"parameter":[37,70],"$":[38,40,44,48,65,67,71,99,109,119],"\\varepsilon":[39,100,120],"{{K_\\mathrm{f}}}^\\star":[45],"/":[46],"{{K_\\mathrm{b}}}^\\star":[47],"characteristic":[51],"conductivities":[53],"domains":[59],"assumed":[61],"to":[62],"scale":[63],"\\varepsilon^\\alpha":[66],"for":[68,124],"\\alpha":[72,110],"\\in":[73],"\\mathbb{R}":[74],"$.":[75,103],"geometry":[78],"parameterized":[80],"aperture":[82],"functions":[83],"on":[84,105],"submanifold":[86],"codimension":[88],"one.":[89],"Given":[90],"fracture,":[92],"we":[93,112,126],"derive":[94],"limit":[96,116],"models":[97,117],"as":[98,118],"\\rightarrow":[101,121],"0":[102,122],"Depending":[104],"value":[107],"$,":[111,123],"obtain":[113],"five":[114],"different":[115],"which":[125],"present":[127],"rigorous":[128],"convergence":[129],"results.&lt;/p&gt;&lt;/abstract&gt;":[130]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
