{"id":"https://openalex.org/W4312140706","doi":"https://doi.org/10.3390/e24121844","title":"A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method","display_name":"A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method","publication_year":2022,"publication_date":"2022-12-18","ids":{"openalex":"https://openalex.org/W4312140706","doi":"https://doi.org/10.3390/e24121844","pmid":"https://pubmed.ncbi.nlm.nih.gov/36554249"},"language":"en","primary_location":{"id":"doi:10.3390/e24121844","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121844","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1844/pdf?version=1671603799","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/12/1844/pdf?version=1671603799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105841341","display_name":"Zhaoxia Meng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaoxia Meng","raw_affiliation_strings":["Department of Energy and Power Engineering, Shanxi Energy Institute, Taiyuan 030024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy and Power Engineering, Shanxi Energy Institute, Taiyuan 030024, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100457582","display_name":"Meng Liu","orcid":"https://orcid.org/0000-0003-4438-0490"},"institutions":[{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meng Liu","raw_affiliation_strings":["School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China","institution_ids":["https://openalex.org/I9086337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102941557","display_name":"Hongen Jia","orcid":"https://orcid.org/0000-0002-4701-4608"},"institutions":[{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongen Jia","raw_affiliation_strings":["School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China","institution_ids":["https://openalex.org/I9086337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102941557"],"corresponding_institution_ids":["https://openalex.org/I9086337"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13869727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"12","first_page":"1844","last_page":"1844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9993000030517578,"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/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.996399998664856,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/liquid-crystal","display_name":"Liquid crystal","score":0.7901029586791992},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.7519917488098145},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6205145120620728},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6152113080024719},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5851812362670898},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.515926718711853},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.48855718970298767},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4427720308303833},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.43401074409484863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4144562780857086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4072074890136719},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.369268000125885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3635771870613098},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3278818130493164},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.24355792999267578},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20037120580673218},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.13734185695648193},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.13666430115699768},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11106228828430176}],"concepts":[{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.7901029586791992},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.7519917488098145},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6205145120620728},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6152113080024719},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5851812362670898},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.515926718711853},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.48855718970298767},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4427720308303833},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.43401074409484863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4144562780857086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4072074890136719},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.369268000125885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3635771870613098},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3278818130493164},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.24355792999267578},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20037120580673218},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.13734185695648193},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.13666430115699768},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11106228828430176},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control 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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24121844","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121844","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1844/pdf?version=1671603799","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:36554249","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36554249","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:858bcadcc6464482b4a724a8bc4b2421","is_oa":true,"landing_page_url":"https://doaj.org/article/858bcadcc6464482b4a724a8bc4b2421","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":"Entropy, Vol 24, Iss 12, p 1844 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/12/1844/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24121844","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":"Entropy; Volume 24; Issue 12; Pages: 1844","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9777973","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9777973","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24121844","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121844","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1844/pdf?version=1671603799","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312140706.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W46161745","https://openalex.org/W130947653","https://openalex.org/W1970849842","https://openalex.org/W2013377070","https://openalex.org/W2032325704","https://openalex.org/W2036617172","https://openalex.org/W2049031884","https://openalex.org/W2065357863","https://openalex.org/W2072060492","https://openalex.org/W2082187902","https://openalex.org/W2084889427","https://openalex.org/W2085042525","https://openalex.org/W2086365560","https://openalex.org/W2091585859","https://openalex.org/W2113913714","https://openalex.org/W2118922968","https://openalex.org/W2135701176","https://openalex.org/W2153986075","https://openalex.org/W2156201971","https://openalex.org/W2963669748","https://openalex.org/W2963702331","https://openalex.org/W4298442294","https://openalex.org/W6601857105","https://openalex.org/W6658797127","https://openalex.org/W6669382727","https://openalex.org/W6680408530"],"related_works":["https://openalex.org/W2018289167","https://openalex.org/W2069570482","https://openalex.org/W2080612831","https://openalex.org/W2018581211","https://openalex.org/W1982804439","https://openalex.org/W3157084023","https://openalex.org/W2094386919","https://openalex.org/W2123791017","https://openalex.org/W4226524568","https://openalex.org/W2371644513"],"abstract_inverted_index":{"In":[0,19],"this":[1],"paper,":[2],"a":[3,11,32,47],"new":[4,33],"decoupling":[5],"method":[6],"is":[7,28],"proposed":[8],"to":[9,73],"solve":[10],"nematic":[12],"liquid":[13],"crystal":[14],"flow":[15],"with":[16],"stretching":[17],"effect.":[18],"the":[20,25,38,53,62,75,81],"finite":[21],"element":[22],"discrete":[23],"framework,":[24],"director":[26],"vector":[27,40],"calculated":[29],"by":[30,46],"introducing":[31],"auxiliary":[34],"variable":[35],"w,":[36],"and":[37,41,57,85,89],"velocity":[39],"scalar":[42],"pressure":[43],"are":[44,65,71],"decoupled":[45],"nonincremental":[48],"pressure-correction":[49],"projection":[50],"method.":[51],"Then,":[52],"energy":[54,59],"dissipation":[55],"law":[56],"unconditional":[58],"stability":[60,84],"of":[61,77],"resulting":[63],"system":[64],"given.":[66],"Finally,":[67],"some":[68],"numerical":[69],"examples":[70],"given":[72],"verify":[74],"effects":[76],"various":[78],"parameters":[79],"on":[80],"singularity":[82],"annihilation,":[83],"accuracy":[86],"in":[87],"space":[88],"time.":[90]},"counts_by_year":[],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}