{"id":"https://openalex.org/W7160399863","doi":"https://doi.org/10.1016/j.camwa.2026.04.030","title":"A lattice Boltzmann method for time-fractional Allen-Cahn equation","display_name":"A lattice Boltzmann method for time-fractional Allen-Cahn equation","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160399863","doi":"https://doi.org/10.1016/j.camwa.2026.04.030"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2026.04.030","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.04.030","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","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/A5135463246","display_name":"Zhi Mao","orcid":"https://orcid.org/0000-0002-7422-7158"},"institutions":[{"id":"https://openalex.org/I144581915","display_name":"Jishou University","ror":"https://ror.org/056szk247","country_code":"CN","type":"education","lineage":["https://openalex.org/I144581915"]},{"id":"https://openalex.org/I4210128208","display_name":"Tongren University","ror":"https://ror.org/035hxad97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210128208"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Mao","raw_affiliation_strings":["School of Data Science, Tongren University, Tongren, 554300, Guizhou, China","School of Mathematics and Statistics, Jishou University, Jishou, 416000, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0002-7422-7158","affiliations":[{"raw_affiliation_string":"School of Data Science, Tongren University, Tongren, 554300, Guizhou, China","institution_ids":["https://openalex.org/I4210128208"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Jishou University, Jishou, 416000, Hunan, China","institution_ids":["https://openalex.org/I144581915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135500857","display_name":"Yi Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I144581915","display_name":"Jishou University","ror":"https://ror.org/056szk247","country_code":"CN","type":"education","lineage":["https://openalex.org/I144581915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Huang","raw_affiliation_strings":["School of Mathematics and Statistics, Jishou University, Jishou, 416000, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Jishou University, Jishou, 416000, Hunan, China","institution_ids":["https://openalex.org/I144581915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135499888","display_name":"Yuan Yu","orcid":"https://orcid.org/0000-0001-5125-2492"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuan Yu","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0001-5125-2492","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046464565","display_name":"Aiguo Xiao","orcid":"https://orcid.org/0000-0003-2075-5040"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aiguo Xiao","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0003-2075-5040","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135518799","display_name":"Haizhuan Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haizhuan Yuan","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411100, Hunan, China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5135499888","https://openalex.org/A5135518799"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":{"value":3170,"currency":"USD","value_usd":3170},"apc_paid":null,"fwci":4.9441,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.94890167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"215","issue":null,"first_page":"122","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9679999947547913,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9679999947547913,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.003000000026077032,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.6539000272750854},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5141000151634216},{"id":"https://openalex.org/keywords/hpp-model","display_name":"HPP model","score":0.43630000948905945},{"id":"https://openalex.org/keywords/bhatnagar\u2013gross\u2013krook-operator","display_name":"Bhatnagar\u2013Gross\u2013Krook operator","score":0.41620001196861267},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.365200012922287},{"id":"https://openalex.org/keywords/direct-simulation-monte-carlo","display_name":"Direct simulation Monte Carlo","score":0.3276999890804291}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6980999708175659},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.6539000272750854},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5141000151634216},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47510001063346863},{"id":"https://openalex.org/C67906445","wikidata":"https://www.wikidata.org/wiki/Q17027724","display_name":"HPP model","level":4,"score":0.43630000948905945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4350000023841858},{"id":"https://openalex.org/C102727969","wikidata":"https://www.wikidata.org/wiki/Q4901423","display_name":"Bhatnagar\u2013Gross\u2013Krook operator","level":5,"score":0.41620001196861267},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34880000352859497},{"id":"https://openalex.org/C164916747","wikidata":"https://www.wikidata.org/wiki/Q4382753","display_name":"Direct simulation Monte Carlo","level":4,"score":0.3276999890804291},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C193999330","wikidata":"https://www.wikidata.org/wiki/Q834200","display_name":"Boltzmann distribution","level":2,"score":0.2775000035762787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.camwa.2026.04.030","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.04.030","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.4600559175014496}],"awards":[{"id":"https://openalex.org/G1129875759","display_name":null,"funder_award_id":"MS (2026) 798","funder_id":"https://openalex.org/F4320322272","funder_display_name":"Guizhou Science and Technology Department"},{"id":"https://openalex.org/G3386244756","display_name":"\u7c98\u5f39\u6027\u6d41\u4f53\u7535\u573a\u54cd\u5e94\u7684\u4ecb\u89c2\u6a21\u578b\u53ca\u5176\u9ad8\u6548\u6570\u503c\u65b9\u6cd5\u7814\u7a76","funder_award_id":"2026JJ60005","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5713074955","display_name":null,"funder_award_id":"12471391","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7030268712","display_name":null,"funder_award_id":"12101527","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322272","display_name":"Guizhou Science and Technology Department","ror":"https://ror.org/00kwnh405"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1993779222","https://openalex.org/W2004277410","https://openalex.org/W2041001120","https://openalex.org/W2046528357","https://openalex.org/W2052725409","https://openalex.org/W2062266804","https://openalex.org/W2062900651","https://openalex.org/W2065300370","https://openalex.org/W2070920957","https://openalex.org/W2130457461","https://openalex.org/W2147722083","https://openalex.org/W2314777371","https://openalex.org/W2327646252","https://openalex.org/W2784259986","https://openalex.org/W2886181830","https://openalex.org/W2955920149","https://openalex.org/W2963309992","https://openalex.org/W2963333609","https://openalex.org/W2964580220","https://openalex.org/W2990575151","https://openalex.org/W2999515346","https://openalex.org/W3018009055","https://openalex.org/W3031710104","https://openalex.org/W3040330965","https://openalex.org/W3061608325","https://openalex.org/W3105047447","https://openalex.org/W3108780065","https://openalex.org/W3134863935","https://openalex.org/W3205272164","https://openalex.org/W4210960748","https://openalex.org/W4224066643","https://openalex.org/W4313595089","https://openalex.org/W4387246044","https://openalex.org/W4394574286","https://openalex.org/W4402458019","https://openalex.org/W4403899542","https://openalex.org/W4404618342","https://openalex.org/W4405955114","https://openalex.org/W4407246622","https://openalex.org/W7119639847","https://openalex.org/W7129667565"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-05-07T00:00:00"}
