{"id":"https://openalex.org/W7141574422","doi":"https://doi.org/10.1016/j.jcp.2026.114887","title":"Energy-Stable, L2-Stable, and weakly H1-Stable BDF2 viscosity splitting method for the penalized incompressible navier\u2013Stokes equations","display_name":"Energy-Stable, L2-Stable, and weakly H1-Stable BDF2 viscosity splitting method for the penalized incompressible navier\u2013Stokes equations","publication_year":2026,"publication_date":"2026-03-27","ids":{"openalex":"https://openalex.org/W7141574422","doi":"https://doi.org/10.1016/j.jcp.2026.114887"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2026.114887","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114887","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"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":"Journal of Computational Physics","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/A5130766608","display_name":"Junxiang Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I111950717","display_name":"Macau University of Science and Technology","ror":"https://ror.org/03jqs2n27","country_code":"MO","type":"education","lineage":["https://openalex.org/I111950717","https://openalex.org/I4391767947"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Junxiang Yang","raw_affiliation_strings":["School of Computer Science and Engineering, Faculty of Innovation Engineering, Special Administrative Region of China, Macau University of Science and Technology, Macao"],"raw_orcid":"https://orcid.org/0009-0006-0062-0017","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Faculty of Innovation Engineering, Special Administrative Region of China, Macau University of Science and Technology, Macao","institution_ids":["https://openalex.org/I111950717"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130816893","display_name":"Yibao Li","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibao Li","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, 710049, China"],"raw_orcid":"https://orcid.org/0000-0002-4847-5430","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130816322","display_name":"Junseok Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Junseok Kim","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0002-0484-9189","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5130816322"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.74166901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"559","issue":null,"first_page":"114887","last_page":"114887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.5659000277519226,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.5659000277519226,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.045899998396635056,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.03849999979138374,"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/viscosity","display_name":"Viscosity","score":0.6234999895095825},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5562999844551086},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.33489999175071716},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.3246000111103058},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.299699991941452},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.2989000082015991}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7372999787330627},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.6234999895095825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5821999907493591},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5562999844551086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4512999951839447},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jcp.2026.114887","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.114887","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"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":"Journal of Computational Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.700839102268219,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W1964126118","https://openalex.org/W1984426476","https://openalex.org/W1994968461","https://openalex.org/W1997815093","https://openalex.org/W2004168836","https://openalex.org/W2011324017","https://openalex.org/W2036955083","https://openalex.org/W2047859546","https://openalex.org/W2076077791","https://openalex.org/W2092284897","https://openalex.org/W2095539128","https://openalex.org/W2097830129","https://openalex.org/W2103556498","https://openalex.org/W2110233871","https://openalex.org/W2123315447","https://openalex.org/W2134781512","https://openalex.org/W2140845715","https://openalex.org/W2146913860","https://openalex.org/W2149087458","https://openalex.org/W2161703460","https://openalex.org/W2242060998","https://openalex.org/W2285972667","https://openalex.org/W2494450351","https://openalex.org/W2766149883","https://openalex.org/W2767124575","https://openalex.org/W2790202791","https://openalex.org/W2798450085","https://openalex.org/W2965650504","https://openalex.org/W2992498009","https://openalex.org/W3108696216","https://openalex.org/W3141019747","https://openalex.org/W3153588574","https://openalex.org/W3173643580","https://openalex.org/W4205629667","https://openalex.org/W4210692496","https://openalex.org/W4214489543","https://openalex.org/W4221139231","https://openalex.org/W4225429166","https://openalex.org/W4226437195","https://openalex.org/W4294916342","https://openalex.org/W4295981439","https://openalex.org/W4301394727","https://openalex.org/W4310082084","https://openalex.org/W4313800227","https://openalex.org/W4366245608","https://openalex.org/W4376111553","https://openalex.org/W4386534878","https://openalex.org/W4387742399","https://openalex.org/W4388741222","https://openalex.org/W4390064200","https://openalex.org/W4391115856","https://openalex.org/W4391132083","https://openalex.org/W4392104192","https://openalex.org/W4392563441","https://openalex.org/W4394681948","https://openalex.org/W4396803490","https://openalex.org/W4401410991","https://openalex.org/W4401697917","https://openalex.org/W4402566306","https://openalex.org/W4403032079","https://openalex.org/W4404019585","https://openalex.org/W4406118826","https://openalex.org/W4406364843","https://openalex.org/W4406420558","https://openalex.org/W4407101573","https://openalex.org/W4407133866","https://openalex.org/W4408161029","https://openalex.org/W4408293817","https://openalex.org/W4408663979","https://openalex.org/W4409186988","https://openalex.org/W4411399794","https://openalex.org/W4411450596"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-04T06:10:10.580331","created_date":"2026-03-28T00:00:00"}