{"id":"https://openalex.org/W2888539694","doi":"https://doi.org/10.1137/17m1145239","title":"Phase-Field Modeling of Two Phase Fluid Filled Fractures in a Poroelastic Medium","display_name":"Phase-Field Modeling of Two Phase Fluid Filled Fractures in a Poroelastic Medium","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2888539694","doi":"https://doi.org/10.1137/17m1145239","mag":"2888539694"},"language":"en","primary_location":{"id":"doi:10.1137/17m1145239","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1145239","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/A5080536862","display_name":"Sanghyun Lee","orcid":"https://orcid.org/0000-0002-2852-3837"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sanghyun Lee","raw_affiliation_strings":["Florida State University [Tallahassee]"],"raw_orcid":"https://orcid.org/0000-0002-2852-3837","affiliations":[{"raw_affiliation_string":"Florida State University [Tallahassee]","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077009185","display_name":"Andro Mikeli\u0107","orcid":"https://orcid.org/0000-0002-4752-8705"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andro Mikeli\u0107","raw_affiliation_strings":["Mod\u00e9lisation math\u00e9matique, calcul scientifique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mod\u00e9lisation math\u00e9matique, calcul scientifique","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003120570","display_name":"Mary F. Wheeler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mary F. Wheeler","raw_affiliation_strings":["Institute for Computational Engineering and Sciences [Austin]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences [Austin]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010756889","display_name":"Thomas Wick","orcid":"https://orcid.org/0000-0002-1102-6332"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Wick","raw_affiliation_strings":["Institut fur angewandte mathematik, Leibniz Universitat Hannover"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut fur angewandte mathematik, Leibniz Universitat Hannover","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.1193,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.98163851,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"16","issue":"4","first_page":"1542","last_page":"1580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"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":0.9980000257492065,"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":0.9970999956130981,"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/poromechanics","display_name":"Poromechanics","score":0.9001306295394897},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.62480628490448},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5721004605293274},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5677393078804016},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5467756986618042},{"id":"https://openalex.org/keywords/fluid-dynamics","display_name":"Fluid dynamics","score":0.4893795847892761},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4850125014781952},{"id":"https://openalex.org/keywords/two-phase-flow","display_name":"Two-phase flow","score":0.46603769063949585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43917039036750793},{"id":"https://openalex.org/keywords/fracture","display_name":"Fracture (geology)","score":0.43533575534820557},{"id":"https://openalex.org/keywords/capillary-pressure","display_name":"Capillary pressure","score":0.4248640239238739},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42447629570961},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37901490926742554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3256901800632477},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3237464427947998},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.273091197013855},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25796639919281006},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.22143104672431946},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.20749342441558838}],"concepts":[{"id":"https://openalex.org/C181965411","wikidata":"https://www.wikidata.org/wiki/Q2314330","display_name":"Poromechanics","level":4,"score":0.9001306295394897},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.62480628490448},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5721004605293274},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5677393078804016},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5467756986618042},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.4893795847892761},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4850125014781952},{"id":"https://openalex.org/C144308804","wikidata":"https://www.wikidata.org/wiki/Q232997","display_name":"Two-phase flow","level":3,"score":0.46603769063949585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43917039036750793},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.43533575534820557},{"id":"https://openalex.org/C48797263","wikidata":"https://www.wikidata.org/wiki/Q4212891","display_name":"Capillary pressure","level":4,"score":0.4248640239238739},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42447629570961},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37901490926742554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3256901800632477},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3237464427947998},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.273091197013855},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25796639919281006},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.22143104672431946},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.20749342441558838},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1145239","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1145239","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":[{"id":"https://metadata.un.org/sdg/6","score":0.6600000262260437,"display_name":"Clean water and sanitation"}],"awards":[{"id":"https://openalex.org/G3469015024","display_name":null,"funder_award_id":"DE FG02-04ER25617","funder_id":"https://openalex.org/F4320337480","funder_display_name":"Basic Energy Sciences"},{"id":"https://openalex.org/G535439220","display_name":null,"funder_award_id":"DE-SC0001114","funder_id":"https://openalex.org/F4320337480","funder_display_name":"Basic Energy Sciences"}],"funders":[{"id":"https://openalex.org/F4320310620","display_name":"University of Texas at Austin","ror":"https://ror.org/00hj54h04"},{"id":"https://openalex.org/F4320337480","display_name":"Basic Energy Sciences","ror":"https://ror.org/05mg91w61"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W112503862","https://openalex.org/W1197273512","https://openalex.org/W1445884928","https://openalex.org/W1506995942","https://openalex.org/W1523953618","https://openalex.org/W1843737582","https://openalex.org/W1967070136","https://openalex.org/W1969593637","https://openalex.org/W1976240542","https://openalex.org/W1979313559","https://openalex.org/W1982518801","https://openalex.org/W1987895449","https://openalex.org/W1989159851","https://openalex.org/W1990319901","https://openalex.org/W1996486047","https://openalex.org/W2005903594","https://openalex.org/W2006064532","https://openalex.org/W2006078294","https://openalex.org/W2008582597","https://openalex.org/W2028784283","https://openalex.org/W2033882205","https://openalex.org/W2034584048","https://openalex.org/W2037372924","https://openalex.org/W2038801387","https://openalex.org/W2043784721","https://openalex.org/W2044751804","https://openalex.org/W2045531090","https://openalex.org/W2045827210","https://openalex.org/W2047336548","https://openalex.org/W2050092501","https://openalex.org/W2058549403","https://openalex.org/W2063550694","https://openalex.org/W2084223864","https://openalex.org/W2086131957","https://openalex.org/W2090397073","https://openalex.org/W2091991433","https://openalex.org/W2094299102","https://openalex.org/W2098137286","https://openalex.org/W2102096503","https://openalex.org/W2105965900","https://openalex.org/W2111879424","https://openalex.org/W2115137311","https://openalex.org/W2126979631","https://openalex.org/W2128946339","https://openalex.org/W2129445590","https://openalex.org/W2130138644","https://openalex.org/W2150207569","https://openalex.org/W2153258731","https://openalex.org/W2155280009","https://openalex.org/W2169599540","https://openalex.org/W2173703816","https://openalex.org/W2187362530","https://openalex.org/W2193211475","https://openalex.org/W2233576873","https://openalex.org/W2239446905","https://openalex.org/W2276196763","https://openalex.org/W2285366996","https://openalex.org/W2301732621","https://openalex.org/W2347487656","https://openalex.org/W2396241390","https://openalex.org/W2399563557","https://openalex.org/W2423814600","https://openalex.org/W2495149401","https://openalex.org/W2501617734","https://openalex.org/W2504723308","https://openalex.org/W2519524256","https://openalex.org/W2524638127","https://openalex.org/W2532317810","https://openalex.org/W2541341587","https://openalex.org/W2542144749","https://openalex.org/W2733987082","https://openalex.org/W2743869222","https://openalex.org/W2745736017","https://openalex.org/W2752809284","https://openalex.org/W2767170238","https://openalex.org/W2790659264","https://openalex.org/W2963558481"],"related_works":["https://openalex.org/W2186710938","https://openalex.org/W2063424227","https://openalex.org/W2902420615","https://openalex.org/W4321996062","https://openalex.org/W2355926219","https://openalex.org/W2387954043","https://openalex.org/W2363277033","https://openalex.org/W2052800072","https://openalex.org/W2071766017","https://openalex.org/W2353091794"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2,24,117],"immiscible":[3],"two":[4,74],"phase":[5,70,75],"flow":[6,28,80,112],"fracture":[7],"model,":[8],"based":[9],"on":[10],"a":[11,58,99,107],"phase-field":[12,55,100],"for":[13],"treating":[14],"crack":[15],"propagation":[16],"in":[17],"porous":[18],"media.":[19],"This":[20],"multifluid":[21],"model":[22,71],"is":[23,57,114],"extension":[25],"of":[26,44,47,60,96],"classical":[27],"models":[29],"and":[30,51,66,86,89,98,120,127],"we":[31,41],"take":[32],"into":[33],"account":[34],"nonzero":[35],"capillary":[36],"pressure.":[37],"Using":[38],"lubrication":[39],"theory,":[40],"provide":[42],"details":[43],"the":[45,64,68,73,78,111,121],"determination":[46],"effective":[48],"parameters:":[49],"absolute":[50],"relative":[52],"permeabilities.":[53],"The":[54,92],"formulation":[56],"generalization":[59],"previous":[61],"works":[62],"by":[63],"authors":[65],"extends":[67],"single":[69],"to":[72],"case.":[76],"Here":[77],"resulting":[79],"system":[81],"has":[82],"four":[83],"unknowns:":[84],"resident":[85],"injected":[87],"pressures":[88],"saturations,":[90],"respectively.":[91],"solid":[93,122],"contribution":[94],"consists":[95],"displacements":[97],"variable.":[101],"Both":[102],"systems":[103],"are":[104,129],"coupled":[105],"employing":[106],"fixed-stress":[108],"splitting.":[109],"Therein,":[110],"problem":[113,123],"treated":[115],"with":[116,131],"iterative":[118],"scheme":[119],"fully":[124],"implicitly.":[125],"Modeling":[126],"algorithms":[128],"substantiated":[130],"several":[132],"numerical":[133],"tests.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
