{"id":"https://openalex.org/W4401994701","doi":"https://doi.org/10.3390/axioms13090587","title":"Combining Glimm\u2019s Scheme and Operator Splitting for Simulating Constrained Flows in Porous Media","display_name":"Combining Glimm\u2019s Scheme and Operator Splitting for Simulating Constrained Flows in Porous Media","publication_year":2024,"publication_date":"2024-08-29","ids":{"openalex":"https://openalex.org/W4401994701","doi":"https://doi.org/10.3390/axioms13090587"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13090587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090587","pdf_url":"https://www.mdpi.com/2075-1680/13/9/587/pdf?version=1724981301","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/9/587/pdf?version=1724981301","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079259348","display_name":"Maria Laura Martins\u2010Costa","orcid":"https://orcid.org/0000-0002-6586-3670"},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Maria Laura Martins-Costa","raw_affiliation_strings":["Laboratory of Theoretical and Applied Mechanics (LMTA), Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da P\u00e1tria, 156, Niter\u00f3i 24210-240, RJ, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6586-3670","affiliations":[{"raw_affiliation_string":"Laboratory of Theoretical and Applied Mechanics (LMTA), Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da P\u00e1tria, 156, Niter\u00f3i 24210-240, RJ, Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020601097","display_name":"Felipe Bastos de Freitas Rachid","orcid":"https://orcid.org/0000-0003-2190-8141"},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Felipe Bastos de Freitas Rachid","raw_affiliation_strings":["Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da P\u00e1tria, 156, Niter\u00f3i 24210-240, RJ, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-2190-8141","affiliations":[{"raw_affiliation_string":"Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da P\u00e1tria, 156, Niter\u00f3i 24210-240, RJ, Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104189382","display_name":"Rog\u00e9rio Pazetto S. da Gama","orcid":null},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rog\u00e9rio Pazetto S. da Gama","raw_affiliation_strings":["Mechanical Engineering Graduate Program (FEN), Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, Rio de Janeiro 20550-013, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Graduate Program (FEN), Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, Rio de Janeiro 20550-013, RJ, Brazil","institution_ids":["https://openalex.org/I40034438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023486098","display_name":"Rog\u00e9rio Martins Saldanha da Gama","orcid":"https://orcid.org/0000-0002-2947-8142"},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rog\u00e9rio M. Saldanha da Gama","raw_affiliation_strings":["Mechanical Engineering Graduate Program (FEN), Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, Rio de Janeiro 20550-013, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering Graduate Program (FEN), Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, Rio de Janeiro 20550-013, RJ, Brazil","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079259348"],"corresponding_institution_ids":["https://openalex.org/I161127581"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.324,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61800844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"13","issue":"9","first_page":"587","last_page":"587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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":0.9988999962806702,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical 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":0.9951000213623047,"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/mathematics","display_name":"Mathematics","score":0.748023509979248},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.546816349029541},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5400024652481079},{"id":"https://openalex.org/keywords/drag","display_name":"Drag","score":0.498854398727417},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.49202772974967957},{"id":"https://openalex.org/keywords/darcys-law","display_name":"Darcy's law","score":0.47817331552505493},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.4728434681892395},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4516177177429199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3977060914039612},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.3387320041656494},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14660409092903137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1327429711818695},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.11558511853218079}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.748023509979248},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.546816349029541},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5400024652481079},{"id":"https://openalex.org/C72921944","wikidata":"https://www.wikidata.org/wiki/Q206621","display_name":"Drag","level":2,"score":0.498854398727417},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.49202772974967957},{"id":"https://openalex.org/C183447037","wikidata":"https://www.wikidata.org/wiki/Q392416","display_name":"Darcy's law","level":4,"score":0.47817331552505493},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.4728434681892395},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4516177177429199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3977060914039612},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.3387320041656494},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14660409092903137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1327429711818695},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.11558511853218079},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13090587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090587","pdf_url":"https://www.mdpi.com/2075-1680/13/9/587/pdf?version=1724981301","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b3c008979ae4486db13102530e54b868","is_oa":true,"landing_page_url":"https://doaj.org/article/b3c008979ae4486db13102530e54b868","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 9, p 587 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/13/9/587/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms13090587","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms13090587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090587","pdf_url":"https://www.mdpi.com/2075-1680/13/9/587/pdf?version=1724981301","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4869293561","display_name":null,"funder_award_id":"304962/2022-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401994701.pdf","grobid_xml":"https://content.openalex.org/works/W4401994701.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W28909584","https://openalex.org/W126332584","https://openalex.org/W1500027774","https://openalex.org/W1965307357","https://openalex.org/W1965504779","https://openalex.org/W1971986192","https://openalex.org/W1973071367","https://openalex.org/W1977896323","https://openalex.org/W1997127260","https://openalex.org/W2010217989","https://openalex.org/W2013535587","https://openalex.org/W2021241760","https://openalex.org/W2032213317","https://openalex.org/W2033315945","https://openalex.org/W2038991247","https://openalex.org/W2043780912","https://openalex.org/W2052183448","https://openalex.org/W2060283935","https://openalex.org/W2064339640","https://openalex.org/W2064522459","https://openalex.org/W2072535043","https://openalex.org/W2088968250","https://openalex.org/W2090674144","https://openalex.org/W2091389150","https://openalex.org/W2100203796","https://openalex.org/W2125276784","https://openalex.org/W2130491327","https://openalex.org/W2131124650","https://openalex.org/W2131820056","https://openalex.org/W2147419294","https://openalex.org/W2156053088","https://openalex.org/W2207027645","https://openalex.org/W2326191714","https://openalex.org/W2566179891","https://openalex.org/W2731561236","https://openalex.org/W3036570908","https://openalex.org/W3103135100","https://openalex.org/W4223459656","https://openalex.org/W4240837102","https://openalex.org/W4249313646","https://openalex.org/W4253538687","https://openalex.org/W4323351126","https://openalex.org/W4388019889","https://openalex.org/W6675026342","https://openalex.org/W6779698875"],"related_works":["https://openalex.org/W2480601066","https://openalex.org/W3174853118","https://openalex.org/W3085759807","https://openalex.org/W1983176903","https://openalex.org/W2083233781","https://openalex.org/W4385807557","https://openalex.org/W4251419119","https://openalex.org/W2079712669","https://openalex.org/W2187649242","https://openalex.org/W3134910861"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"constrained":[3],"Newtonian":[4],"fluid":[5],"flows":[6],"through":[7],"porous":[8,53],"media,":[9],"accounting":[10],"for":[11,28,93,143,166,189],"the":[12,16,29,37,43,60,94,101,105,133,167,172,175,190,196,199,206],"drag":[13,147,203],"effect":[14],"on":[15,205],"fluid,":[17],"modeled":[18],"using":[19,154],"a":[20,25,31,76,155],"Mixture":[21],"Theory":[22],"perspective":[23],"and":[24,33,59,96,145,181,201],"constitutive":[26,164],"relation":[27,165],"pressure\u2014namely,":[30],"continuous":[32],"differentiable":[34],"function":[35,170],"of":[36,159,171,198],"saturation":[38],"that":[39,99],"ensures":[40],"always":[41],"preserving":[42],"problem":[44],"hyperbolicity.":[45],"The":[46,70,163,193],"pressure":[47],"equation":[48],"also":[49,178],"permits":[50],"an":[51,88,122],"ultra-small":[52],"matrix":[54],"supersaturation":[55],"(that":[56],"is":[57,111,135],"controlled)":[58],"transition":[61],"from":[62],"unsaturated":[63],"to":[64,75,91,114,141,185],"saturated":[65],"flow":[66],"(and":[67],"vice":[68],"versa).":[69],"mathematical":[71],"model":[72],"gives":[73],"rise":[74],"nonlinear,":[77],"non-homogeneous":[78,116],"hyperbolic":[79,117],"system.":[80],"Its":[81],"numerical":[82],"simulation":[83],"combines":[84],"Glimm\u2019s":[85,137,149],"method":[86,138],"with":[87,121,139,174],"operator-splitting":[89,123,140],"strategy":[90],"account":[92,142],"Darcy":[95,200],"Forchheimer":[97,202],"terms":[98,204],"cause":[100],"system\u2019s":[102],"non-homogeneity.":[103],"Despite":[104],"Glimm":[106],"method\u2019s":[107],"proven":[108],"convergence,":[109],"it":[110],"not":[112],"adequate":[113],"approximate":[115],"systems":[118],"unless":[119],"combined":[120],"technique.":[124],"Although":[125],"other":[126],"approaches":[127],"have":[128],"already":[129],"addressed":[130],"this":[131],"problem,":[132],"novelty":[134],"combining":[136],"linear":[144],"nonlinear":[146],"effects.":[148],"scheme":[150],"marches":[151],"in":[152],"time":[153],"formerly":[156],"selected":[157],"number":[158],"associated":[160],"Riemann":[161,191],"problems.":[162],"pressure\u2014an":[168],"increasing":[169],"saturation,":[173],"first":[176],"derivative":[177],"increasing,":[179],"convex,":[180],"positive,":[182],"enables":[183],"us":[184],"obtain":[186],"explicit":[187],"expressions":[188],"invariants.":[192],"results":[194],"show":[195],"influence":[197],"flow.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-05T09:01:59.212387","created_date":"2025-10-10T00:00:00"}
