{"id":"https://openalex.org/W3115006473","doi":"https://doi.org/10.1080/00207160.2020.1870680","title":"Characteristic-based finite-difference schemes for the simulation of convection\u2013diffusion equation by the finite-difference-based lattice Boltzmann methods","display_name":"Characteristic-based finite-difference schemes for the simulation of convection\u2013diffusion equation by the finite-difference-based lattice Boltzmann methods","publication_year":2020,"publication_date":"2020-12-30","ids":{"openalex":"https://openalex.org/W3115006473","doi":"https://doi.org/10.1080/00207160.2020.1870680","mag":"3115006473"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2020.1870680","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1870680","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5003180256","display_name":"Gerasim V. Krivovichev","orcid":"https://orcid.org/0000-0002-1135-1469"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"G. V. Krivovichev","raw_affiliation_strings":["Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes, Saint Petersburg, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes, Saint Petersburg, Russian Federation","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003180256"],"corresponding_institution_ids":["https://openalex.org/I172901346"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15358053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"98","issue":"10","first_page":"1991","last_page":"2007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":1.0,"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":1.0,"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/T12163","display_name":"Aerosol Filtration and Electrostatic Precipitation","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9815000295639038,"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/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.7996993660926819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.783623218536377},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.7195485830307007},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.7091823816299438},{"id":"https://openalex.org/keywords/finite-difference-coefficient","display_name":"Finite difference coefficient","score":0.6630841493606567},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.5249666571617126},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5030893683433533},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4843088686466217},{"id":"https://openalex.org/keywords/numerical-solution-of-the-convection\u2013diffusion-equation","display_name":"Numerical solution of the convection\u2013diffusion equation","score":0.42954832315444946},{"id":"https://openalex.org/keywords/lattice-gas-automaton","display_name":"Lattice gas automaton","score":0.41972970962524414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4165458381175995},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.41337817907333374},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39869678020477295},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36929529905319214},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.26330018043518066},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.14845013618469238},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14776667952537537},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14714527130126953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10327476263046265},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07605662941932678}],"concepts":[{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.7996993660926819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.783623218536377},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.7195485830307007},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.7091823816299438},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.6630841493606567},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.5249666571617126},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5030893683433533},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4843088686466217},{"id":"https://openalex.org/C101303905","wikidata":"https://www.wikidata.org/wiki/Q17104838","display_name":"Numerical solution of the convection\u2013diffusion equation","level":4,"score":0.42954832315444946},{"id":"https://openalex.org/C156890611","wikidata":"https://www.wikidata.org/wiki/Q3099721","display_name":"Lattice gas automaton","level":4,"score":0.41972970962524414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4165458381175995},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.41337817907333374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39869678020477295},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36929529905319214},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.26330018043518066},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.14845013618469238},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14776667952537537},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14714527130126953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10327476263046265},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07605662941932678},{"id":"https://openalex.org/C192499940","wikidata":"https://www.wikidata.org/wiki/Q17022326","display_name":"Stochastic cellular automaton","level":3,"score":0.0},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2020.1870680","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1870680","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W72036692","https://openalex.org/W113976918","https://openalex.org/W863967364","https://openalex.org/W1966007058","https://openalex.org/W1977754882","https://openalex.org/W1978300980","https://openalex.org/W1979920761","https://openalex.org/W1983130239","https://openalex.org/W1983265956","https://openalex.org/W1984684385","https://openalex.org/W1990050218","https://openalex.org/W1996325534","https://openalex.org/W1999380124","https://openalex.org/W2005124716","https://openalex.org/W2009420423","https://openalex.org/W2025723755","https://openalex.org/W2026838161","https://openalex.org/W2049093178","https://openalex.org/W2050575358","https://openalex.org/W2066557181","https://openalex.org/W2071909711","https://openalex.org/W2107038094","https://openalex.org/W2122608714","https://openalex.org/W2201313735","https://openalex.org/W2480862060","https://openalex.org/W2538167577","https://openalex.org/W2611013241","https://openalex.org/W2790333933","https://openalex.org/W2796255898","https://openalex.org/W2802601743","https://openalex.org/W3005239502","https://openalex.org/W3106170021","https://openalex.org/W4254345639"],"related_works":["https://openalex.org/W2372700288","https://openalex.org/W4313290838","https://openalex.org/W2027689510","https://openalex.org/W2387034630","https://openalex.org/W2038254731","https://openalex.org/W3161316917","https://openalex.org/W2015391089","https://openalex.org/W3115006473","https://openalex.org/W2370479547","https://openalex.org/W2037533572"],"abstract_inverted_index":{"The":[0,35,45],"paper":[1],"is":[2,38,54,101,119,139],"devoted":[3],"to":[4,30],"the":[5,12,15,19,27,41,49,57,60,69,72,76,81,84,89,92,96,104,109,114,121,128,131,136],"analysis":[6,37],"of":[7,14,48,59,91,108,130],"characteristic-based":[8],"(CB)":[9],"schemes":[10,25,50,65,110,123],"for":[11,63,71,127],"simulation":[13],"convection\u2013diffusion":[16],"equation":[17],"by":[18,40,75],"lattice":[20],"Boltzmann":[21],"method":[22],"(LBM).":[23],"Numerical":[24],"from":[26],"first":[28],"order":[29],"fourth":[31],"one":[32],"are":[33,51,66,111],"considered.":[34],"stability":[36,46,61],"realized":[39],"von":[42],"Neumann":[43],"method.":[44],"domains":[47,62,70],"constructed.":[52],"It":[53],"demonstrated":[55,102],"that":[56,103],"areas":[58],"CB":[64],"larger":[67],"than":[68],"schemes,":[73],"constructed":[74],"traditional":[77],"approach,":[78],"based":[79],"on":[80],"discretization":[82],"at":[83],"Cartesian":[85],"axes":[86],"directions.":[87],"By":[88],"solution":[90],"numerical":[93],"examples":[94],"with":[95,113],"smooth":[97],"initial":[98],"conditions,":[99],"it":[100,118],"practical":[105],"convergence":[106],"rates":[107],"consistent":[112],"theoretical":[115],"values.":[116],"As":[117],"shown,":[120],"proposed":[122],"can":[124],"be":[125],"used":[126],"cases":[129],"Peclet":[132],"number":[133],"values,":[134],"when":[135],"classical":[137],"LBM":[138],"unstable.":[140]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
