{"id":"https://openalex.org/W2041064645","doi":"https://doi.org/10.1155/2013/478054","title":"Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model","display_name":"Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2041064645","doi":"https://doi.org/10.1155/2013/478054","mag":"2041064645"},"language":"en","primary_location":{"id":"doi:10.1155/2013/478054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/478054","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/478054.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/478054.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102907030","display_name":"Guang-an Zou","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210101167","display_name":"Institute of Oceanology","ror":"https://ror.org/018yw5541","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210101167"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guang-an Zou","raw_affiliation_strings":["Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China","University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0003-2350-2030","affiliations":[{"raw_affiliation_string":"Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China","institution_ids":["https://openalex.org/I4210101167","https://openalex.org/I19820366"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100728790","display_name":"Bo Wang","orcid":"https://orcid.org/0000-0003-4073-1599"},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Wang","raw_affiliation_strings":["Institute of Applied Mathematics, Henan University, Kaifeng 475004, China"],"raw_orcid":"https://orcid.org/0000-0003-4073-1599","affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Henan University, Kaifeng 475004, China","institution_ids":["https://openalex.org/I173899330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110659314","display_name":"Mu Mu","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210101167","display_name":"Institute of Oceanology","ror":"https://ror.org/018yw5541","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210101167"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mu Mu","raw_affiliation_strings":["Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China","institution_ids":["https://openalex.org/I4210101167","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110659314"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210101167"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08250249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7509934902191162},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7023870944976807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6191553473472595},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.572400689125061},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5244017839431763},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5216365456581116},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.49214357137680054},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46400633454322815},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4582606256008148},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"Shallow water equations","score":0.45233580470085144},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43303436040878296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4145236015319824},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1956944763660431},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.19336143136024475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1332925260066986}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7509934902191162},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7023870944976807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6191553473472595},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.572400689125061},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5244017839431763},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5216365456581116},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.49214357137680054},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46400633454322815},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4582606256008148},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.45233580470085144},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43303436040878296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4145236015319824},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1956944763660431},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.19336143136024475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1332925260066986},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/478054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/478054","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/478054.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808190","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808190","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:478054","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/478054.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:183fbde6967a4e30b5906eba83bba558","is_oa":true,"landing_page_url":"https://doaj.org/article/183fbde6967a4e30b5906eba83bba558","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/478054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/478054","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/478054.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G1255778228","display_name":null,"funder_award_id":"41230420","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1597794467","display_name":null,"funder_award_id":"2012CB417404","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3291724298","display_name":null,"funder_award_id":"11-1-4-95-jch","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7322575742","display_name":null,"funder_award_id":"2012CB417404","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/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2041064645.pdf","grobid_xml":"https://content.openalex.org/works/W2041064645.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W70323760","https://openalex.org/W603376266","https://openalex.org/W1015323304","https://openalex.org/W1509146450","https://openalex.org/W1519793694","https://openalex.org/W1529100907","https://openalex.org/W1601755832","https://openalex.org/W1607405879","https://openalex.org/W1968642437","https://openalex.org/W1971680876","https://openalex.org/W1973101332","https://openalex.org/W1973385488","https://openalex.org/W1998187039","https://openalex.org/W2014688297","https://openalex.org/W2016730552","https://openalex.org/W2017971309","https://openalex.org/W2020863487","https://openalex.org/W2024219079","https://openalex.org/W2027370888","https://openalex.org/W2028174880","https://openalex.org/W2031027147","https://openalex.org/W2037019252","https://openalex.org/W2038176330","https://openalex.org/W2041658336","https://openalex.org/W2044962590","https://openalex.org/W2053544623","https://openalex.org/W2055883962","https://openalex.org/W2069923634","https://openalex.org/W2087910137","https://openalex.org/W2098076232","https://openalex.org/W2106247461","https://openalex.org/W2109828313","https://openalex.org/W2109940529","https://openalex.org/W2144852980","https://openalex.org/W2158531045","https://openalex.org/W2159752342","https://openalex.org/W2160804430","https://openalex.org/W2163783206","https://openalex.org/W2163827223","https://openalex.org/W2165533812","https://openalex.org/W2166309152","https://openalex.org/W2175499570","https://openalex.org/W2175606803","https://openalex.org/W4205698215"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2516036415","https://openalex.org/W2493718600"],"abstract_inverted_index":{"A":[0,56],"1.5-layer":[1],"reduced-gravity":[2],"shallow-water":[3],"ocean":[4,121],"model":[5,70,111],"in":[6,13],"spherical":[7],"coordinates":[8],"is":[9,43,75,113,115],"described":[10],"and":[11,26,69,89,94,109],"discretized":[12],"a":[14],"staggered":[15],"grid":[16],"(standard":[17],"Arakawa":[18],"C-grid)":[19],"with":[20,38],"the":[21,27,39,47,65,85,120],"forward-time":[22],"central-space":[23],"(FTCS)":[24],"method":[25,36],"Leap-frog":[28],"finite":[29,52],"difference":[30,53],"scheme.":[31],"The":[32],"discrete":[33],"Fourier":[34],"analysis":[35],"combined":[37],"Gershgorin":[40],"circle":[41],"theorem":[42],"used":[44,117],"to":[45,104,118],"study":[46],"stability":[48,79,107],"of":[49,58,61],"these":[50,78],"two":[51,91],"numerical":[54,110],"models.":[55],"series":[57],"necessary":[59],"conditions":[60,80],"selection":[62],"criteria":[63],"for":[64],"time-space":[66],"step":[67],"sizes":[68],"parameters":[71],"are":[72,81,102],"obtained.":[73],"It":[74],"showed":[76],"that":[77,112],"more":[82],"accurate":[83],"than":[84],"Courant-Friedrichs-Lewy":[86],"(CFL)":[87],"condition":[88],"other":[90],"criterions":[92],"(Blumberg":[93],"Mellor,":[95],"1987;":[96],"Casulli,":[97],"1990,":[98],"1992).":[99],"Numerical":[100],"experiments":[101],"proposed":[103],"test":[105],"our":[106],"results,":[108],"designed":[114],"also":[116],"simulate":[119],"current.":[122]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
