{"id":"https://openalex.org/W2922279583","doi":"https://doi.org/10.1137/17m1160744","title":"Control Volume Approximation of Degenerate Two-Phase Porous Flows","display_name":"Control Volume Approximation of Degenerate Two-Phase Porous Flows","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2922279583","doi":"https://doi.org/10.1137/17m1160744","mag":"2922279583"},"language":"en","primary_location":{"id":"doi:10.1137/17m1160744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160744","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":"SIAM Journal on Numerical Analysis","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/A5022547833","display_name":"T. J. Murphy","orcid":"https://orcid.org/0000-0002-6137-9873"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas J. Murphy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042222077","display_name":"Noel J. Walkington","orcid":"https://orcid.org/0000-0002-9128-0524"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Noel J. Walkington","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7105,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72142028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"57","issue":"2","first_page":"527","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9984999895095825,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8199859857559204},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7006022334098816},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6553284525871277},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5783588886260986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5503302812576294},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5012631416320801},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47337692975997925},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46506860852241516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4622464179992676},{"id":"https://openalex.org/keywords/euler\u2013lagrange-equation","display_name":"Euler\u2013Lagrange equation","score":0.45739731192588806},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.4452468454837799},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.42717245221138},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.2846795320510864},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1532963514328003},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1519545614719391},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09082245826721191},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.06506851315498352}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8199859857559204},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7006022334098816},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6553284525871277},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5783588886260986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5503302812576294},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5012631416320801},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47337692975997925},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46506860852241516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4622464179992676},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.45739731192588806},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4452468454837799},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.42717245221138},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.2846795320510864},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1532963514328003},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1519545614719391},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09082245826721191},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.06506851315498352},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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:10.1137/17m1160744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1160744","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5428845887","display_name":"Analysis of Algorithms for Simulating Macroscopic Material Response","funder_award_id":"1418991","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5820970597","display_name":"DMREF: Collaborative Research: Materials Engineering of Columnar and Living Liquid Crystals via Experimental Characterization, Mathematical Modeling, and Simulation","funder_award_id":"1729478","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310207","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1507163784","https://openalex.org/W1559735195","https://openalex.org/W1576627634","https://openalex.org/W1986490170","https://openalex.org/W2016800253","https://openalex.org/W2020982326","https://openalex.org/W2046358818","https://openalex.org/W2052711668","https://openalex.org/W2053987804","https://openalex.org/W2054723044","https://openalex.org/W2056700535","https://openalex.org/W2060866894","https://openalex.org/W2062294426","https://openalex.org/W2071048859","https://openalex.org/W2074110915","https://openalex.org/W2075224881","https://openalex.org/W2085677930","https://openalex.org/W2086131957","https://openalex.org/W2122552271","https://openalex.org/W2325176099","https://openalex.org/W2505352333","https://openalex.org/W2563302637","https://openalex.org/W2801872526","https://openalex.org/W3101705151"],"related_works":["https://openalex.org/W2024346620","https://openalex.org/W4241530481","https://openalex.org/W2009711572","https://openalex.org/W1981367860","https://openalex.org/W2365810470","https://openalex.org/W1674877062","https://openalex.org/W2158188297","https://openalex.org/W2039043967","https://openalex.org/W2501406218","https://openalex.org/W2225139434"],"abstract_inverted_index":{"Implicit":[0],"Euler":[1],"approximations":[2,51],"of":[3,10,22,46],"the":[4,7,19],"equations":[5,21],"governing":[6],"porous":[8],"flow":[9],"two":[11],"immiscible":[12],"incompressible":[13],"fluids":[14],"are":[15,30,52],"shown":[16],"to":[17,33,48],"be":[18],"Euler--Lagrange":[20],"a":[23],"convex":[24,28],"function.":[25],"Tools":[26],"from":[27],"analysis":[29],"then":[31],"used":[32],"develop":[34],"robust":[35],"fully":[36],"discrete":[37],"algorithms":[38],"for":[39],"their":[40],"numerical":[41],"approximation.":[42],"Existence":[43],"and":[44],"uniqueness":[45],"solutions":[47],"control":[49],"volume":[50],"established.":[53]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}