{"id":"https://openalex.org/W2963769992","doi":"https://doi.org/10.1515/jnum-2012-0016","title":"Solution of 2D Boussinesq systems with freefem++: the flat bottom case","display_name":"Solution of 2D Boussinesq systems with freefem++: the flat bottom case","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2963769992","doi":"https://doi.org/10.1515/jnum-2012-0016","mag":"2963769992"},"language":"en","primary_location":{"id":"doi:10.1515/jnum-2012-0016","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnum-2012-0016","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical 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/A5029537797","display_name":"Georges Sadaka","orcid":"https://orcid.org/0000-0003-4708-3598"},"institutions":[{"id":"https://openalex.org/I4647051","display_name":"Universit\u00e9 de Picardie Jules Verne","ror":"https://ror.org/01gyxrk03","country_code":"FR","type":"education","lineage":["https://openalex.org/I4647051"]},{"id":"https://openalex.org/I4210163673","display_name":"Laboratoire Ami\u00e9nois de Math\u00e9matique Fondamentale et Appliqu\u00e9e","ror":"https://ror.org/04smxbm79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210163673","https://openalex.org/I4647051"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"G. Sadaka","raw_affiliation_strings":["Universit\u00b4e de Picardie Jules Verne, LAMFA CNRS UMR 7352, 33, rue Saint-Leu, 80039 Amiens, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00b4e de Picardie Jules Verne, LAMFA CNRS UMR 7352, 33, rue Saint-Leu, 80039 Amiens, France","institution_ids":["https://openalex.org/I4210163673","https://openalex.org/I4647051","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029537797"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210163673","https://openalex.org/I4647051"],"apc_list":null,"apc_paid":null,"fwci":0.2968,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.6880282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"3-4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9944999814033508,"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/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9944999814033508,"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/T10647","display_name":"Coastal and Marine Dynamics","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9854999780654907,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8521212339401245},{"id":"https://openalex.org/keywords/boussinesq-approximation","display_name":"Boussinesq approximation (buoyancy)","score":0.740308403968811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7221875190734863},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.53630530834198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45940154790878296},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1353282630443573},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11537227034568787}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8521212339401245},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.740308403968811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7221875190734863},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.53630530834198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45940154790878296},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1353282630443573},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11537227034568787},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.0},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.0},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jnum-2012-0016","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnum-2012-0016","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.757.1350","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.757.1350","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1205.3147.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1969779317","https://openalex.org/W2033786733","https://openalex.org/W2038081758","https://openalex.org/W2065282166","https://openalex.org/W2065348520","https://openalex.org/W2069892416","https://openalex.org/W2089825483","https://openalex.org/W2091735769","https://openalex.org/W2121115811","https://openalex.org/W2143167560","https://openalex.org/W2161503067","https://openalex.org/W4292166829","https://openalex.org/W4383750633"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1979597421","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W2007980826","https://openalex.org/W946352265","https://openalex.org/W2519394870","https://openalex.org/W2893458136"],"abstract_inverted_index":{"Abstract-":[0],"We":[1,52,86],"consider":[2],"here":[3,54],"different":[4,115],"family":[5,117],"of":[6,22,32,36,90,102,111,128],"Boussinesq":[7,116],"systems":[8,14,63,73],"in":[9,39,50,76,84],"two":[10],"space":[11,77],"dimensions.":[12],"These":[13],"approximate":[15],"the":[16,88,103,112,129],"three-dimensional":[17],"Euler":[18],"equations":[19,28],"and":[20,46,78,108],"consist":[21],"three":[23],"coupled":[24],"nonlinear":[25],"dispersive":[26],"wave":[27],"that":[29],"describe":[30],"propagation":[31],"long":[33],"surface":[34],"waves":[35],"small":[37],"amplitude":[38],"ideal":[40],"fluids":[41],"over":[42],"a":[43,55,65,79,96,109],"horizontal":[44],"bottom":[45],"which":[47],"was":[48,74],"studied":[49],"[7,9,10].":[51],"present":[53],"FreeFem++":[56],"code":[57,92],"aimed":[58],"at":[59],"solving":[60],"numerically":[61],"these":[62,72],"where":[64,93],"discretization":[66],"using":[67],"P1":[68],"finite":[69],"element":[70],"for":[71,114],"taken":[75],"second":[80],"order":[81],"Runge-Kutta":[82],"scheme":[83],"time.":[85],"give":[87],"detail":[89],"our":[91],"we":[94,123],"use":[95],"mesh":[97],"adaptation":[98],"technique.":[99],"An":[100],"optimization":[101],"used":[104],"algorithm":[105],"is":[106,118],"done":[107,119],"comparison":[110],"solution":[113],"too.":[120],"The":[121],"results":[122],"obtained":[124],"agree":[125],"with":[126],"those":[127],"literature.":[130]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-02T08:37:19.008085","created_date":"2025-10-10T00:00:00"}