{"id":"https://openalex.org/W4411328253","doi":"https://doi.org/10.1080/00207160.2025.2518277","title":"Theoretical analysis of second-order modified upwind conservative characteristic finite difference for advection diffusion equations","display_name":"Theoretical analysis of second-order modified upwind conservative characteristic finite difference for advection diffusion equations","publication_year":2025,"publication_date":"2025-06-16","ids":{"openalex":"https://openalex.org/W4411328253","doi":"https://doi.org/10.1080/00207160.2025.2518277"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2025.2518277","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2025.2518277","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":null,"display_name":"Xinjing Han","orcid":null},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinjing Han","raw_affiliation_strings":["Shandong Agricultural University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100558075","display_name":"Zhongguo Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongguo Zhou","raw_affiliation_strings":["Shandong Agricultural University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056602636","display_name":"Hao Pan","orcid":"https://orcid.org/0000-0003-3628-9777"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Pan","raw_affiliation_strings":["Shandong Agricultural University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100675540","display_name":"Wang Yan","orcid":"https://orcid.org/0000-0001-7749-0448"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Wang","raw_affiliation_strings":["Shandong Agricultural University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shandong Agricultural University","institution_ids":["https://openalex.org/I74485261"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100558075"],"corresponding_institution_ids":["https://openalex.org/I74485261"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10236415,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"102","issue":"11","first_page":"1758","last_page":"1785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9980999827384949,"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/upwind-scheme","display_name":"Upwind scheme","score":0.8909674882888794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7845417261123657},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.6832537651062012},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.6000368595123291},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5514526963233948},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5131235718727112},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4939139485359192},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4781162142753601},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46284645795822144},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4473419189453125},{"id":"https://openalex.org/keywords/numerical-diffusion","display_name":"Numerical diffusion","score":0.42944738268852234},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3292234539985657},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2991430163383484},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13766610622406006},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.10654965043067932},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07042267918586731}],"concepts":[{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.8909674882888794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7845417261123657},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.6832537651062012},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.6000368595123291},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5514526963233948},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5131235718727112},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4939139485359192},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4781162142753601},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46284645795822144},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4473419189453125},{"id":"https://openalex.org/C148444096","wikidata":"https://www.wikidata.org/wiki/Q7069655","display_name":"Numerical diffusion","level":2,"score":0.42944738268852234},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3292234539985657},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2991430163383484},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13766610622406006},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.10654965043067932},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07042267918586731},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2025.2518277","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2025.2518277","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":[{"display_name":"Climate action","score":0.6600000262260437,"id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G739448733","display_name":null,"funder_award_id":"61703250","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W593406250","https://openalex.org/W656657393","https://openalex.org/W1499976760","https://openalex.org/W1972822338","https://openalex.org/W1980787167","https://openalex.org/W1986618291","https://openalex.org/W2022390295","https://openalex.org/W2028230944","https://openalex.org/W2032496201","https://openalex.org/W2052167222","https://openalex.org/W2069390628","https://openalex.org/W2073945818","https://openalex.org/W2212739564","https://openalex.org/W2593049247","https://openalex.org/W2989106239","https://openalex.org/W4393392682","https://openalex.org/W4403230339"],"related_works":["https://openalex.org/W2335346359","https://openalex.org/W2071529178","https://openalex.org/W1988702003","https://openalex.org/W3029277752","https://openalex.org/W1972136974","https://openalex.org/W2051819179","https://openalex.org/W2076449385","https://openalex.org/W1979604782","https://openalex.org/W1985883026","https://openalex.org/W2358755944"],"abstract_inverted_index":{"A":[0],"spatial":[1],"second-order":[2,37,86],"conservation":[3],"characteristic":[4],"finite":[5],"difference":[6],"method":[7],"is":[8,84],"developed":[9],"to":[10,80],"solve":[11],"advection-diffusion":[12],"equations":[13],"on":[14,47],"the":[15,26,29,36,42,52,55,59],"Lagrangian":[16],"grid.":[17],"The":[18,44,61],"intermediate":[19],"numerical":[20,76],"solutions":[21],"are":[22,33,49,65,78],"first":[23],"computed":[24,50],"with":[25,51],"integration":[27,53],"of":[28,54,85],"parabolic":[30,56],"interpolation,":[31],"which":[32],"solved":[34],"by":[35,71],"modified":[38],"upwind":[39],"scheme":[40,83],"along":[41,58],"x-direction.":[43],"mass":[45],"M\u00afi,jn":[46],"\u03a9\u00afi,j(tn)":[48],"interpolation":[57],"y-direction.":[60],"stability":[62],"and":[63,90],"convergence":[64],"strictly":[66],"proved":[67],"in":[68,88,93],"L2":[69],"norm":[70],"some":[72],"auxiliary":[73],"lemmas.":[74],"Some":[75],"experiments":[77],"used":[79],"test":[81],"our":[82],"convergent":[87,92],"space":[89],"first-order":[91],"time.":[94]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}