{"id":"https://openalex.org/W4399877415","doi":"https://doi.org/10.1090/mcom/4088","title":"An entropy-stable and fully well-balanced scheme for the Euler equations with gravity","display_name":"An entropy-stable and fully well-balanced scheme for the Euler equations with gravity","publication_year":2024,"publication_date":"2024-06-21","ids":{"openalex":"https://openalex.org/W4399877415","doi":"https://doi.org/10.1090/mcom/4088"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2406.15051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.15051","pdf_url":"https://arxiv.org/pdf/2406.15051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2406.15051","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103257701","display_name":"Christophe Berthon","orcid":"https://orcid.org/0000-0003-3999-3479"},"institutions":[{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Berthon, Christophe","raw_affiliation_strings":["LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","institution_ids":["https://openalex.org/I4210153365"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086114809","display_name":"Victor Michel-Dansac","orcid":"https://orcid.org/0000-0002-3859-8517"},"institutions":[{"id":"https://openalex.org/I4210118362","display_name":"Institut de Recherche Math\u00e9matique Avanc\u00e9e","ror":"https://ror.org/02hwgty18","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210118362","https://openalex.org/I4210141950","https://openalex.org/I68947357"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michel-Dansac, Victor","raw_affiliation_strings":["MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (Centre Inria de l'Universit\u00e9 de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-l\u00e8s-Nancy - France)","IRMA - Institut de Recherche Math\u00e9matique Avanc\u00e9e (7 rue Ren\u00e9-Descartes, 67084 Strasbourg Cedex, France - France)","MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (Centre Inria de l'Universit\u00e9 de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-l\u00e8s-Nancy - France)","institution_ids":["https://openalex.org/I90183372"]},{"raw_affiliation_string":"IRMA - Institut de Recherche Math\u00e9matique Avanc\u00e9e (7 rue Ren\u00e9-Descartes, 67084 Strasbourg Cedex, France - France)","institution_ids":["https://openalex.org/I4210118362"]},{"raw_affiliation_string":"MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075033730","display_name":"Andrea Thomann","orcid":"https://orcid.org/0000-0001-9195-0404"},"institutions":[{"id":"https://openalex.org/I4210118362","display_name":"Institut de Recherche Math\u00e9matique Avanc\u00e9e","ror":"https://ror.org/02hwgty18","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210118362","https://openalex.org/I4210141950","https://openalex.org/I68947357"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thomann, Andrea","raw_affiliation_strings":["MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (Centre Inria de l'Universit\u00e9 de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-l\u00e8s-Nancy - France)","IRMA - Institut de Recherche Math\u00e9matique Avanc\u00e9e (7 rue Ren\u00e9-Descartes, 67084 Strasbourg Cedex, France - France)","MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (Centre Inria de l'Universit\u00e9 de Lorraine , 615 Rue du Jardin-Botanique, 54600 Villers-l\u00e8s-Nancy - France)","institution_ids":["https://openalex.org/I90183372"]},{"raw_affiliation_string":"IRMA - Institut de Recherche Math\u00e9matique Avanc\u00e9e (7 rue Ren\u00e9-Descartes, 67084 Strasbourg Cedex, France - France)","institution_ids":["https://openalex.org/I4210118362"]},{"raw_affiliation_string":"MACARON - Apprentissage automatique pour des m\u00e9thodes num\u00e9riques optimis\u00e9es (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9927999973297119,"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":0.9927999973297119,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9593999981880188,"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/eulers-formula","display_name":"Euler's formula","score":0.6315101981163025},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5837975740432739},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5542815327644348},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5260367393493652},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4996936321258545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4063371419906616},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27653026580810547},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25027358531951904},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.16449233889579773}],"concepts":[{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6315101981163025},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5837975740432739},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5542815327644348},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5260367393493652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4996936321258545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4063371419906616},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27653026580810547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25027358531951904},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16449233889579773}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2406.15051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.15051","pdf_url":"https://arxiv.org/pdf/2406.15051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04620125v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04620125","pdf_url":"https://hal.science/hal-04620125/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2406.15051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2406.15051","pdf_url":"https://arxiv.org/pdf/2406.15051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4415361394","display_name":"Producing trustworthy high-performance code via source-to-source transformations","funder_award_id":"ANR-22-CE25-0017","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6582100286","display_name":"MUltiscale and treFFtz for numerIcal traNsport","funder_award_id":"ANR-19-CE46-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399877415.pdf","grobid_xml":"https://content.openalex.org/works/W4399877415.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1975289146","https://openalex.org/W2105887828","https://openalex.org/W2931831557","https://openalex.org/W2563697776","https://openalex.org/W3124634719","https://openalex.org/W4300998095","https://openalex.org/W1498128986","https://openalex.org/W4297915718","https://openalex.org/W2388608635","https://openalex.org/W2357986411"],"abstract_inverted_index":{"The":[0,23],"present":[1],"work":[2],"concerns":[3],"the":[4,15,46,54,58,77,81,84,98,101,113],"derivation":[5],"of":[6,14,80,86,100],"a":[7,19],"numerical":[8,95,103],"scheme":[9,25,60],"to":[10,28,36,75,107],"approximate":[11,82,88],"weak":[12],"solutions":[13,49],"Euler":[16],"equations":[17],"with":[18],"gravitational":[20],"source":[21],"term.":[22],"designed":[24],"is":[26,34,61,92,110],"proved":[27],"be":[29],"fully":[30,67],"well-balanced":[31],"since":[32,63],"it":[33,64],"able":[35],"exactly":[37],"preserve":[38],"all":[39,66],"moving":[40],"equilibrium":[41],"solutions,":[42,83],"as":[43,45],"well":[44],"corresponding":[47],"steady":[48],"at":[50],"rest":[51],"obtained":[52],"when":[53],"velocity":[55],"vanishes.":[56],"Moreover,":[57],"proposed":[59],"entropy-preserving":[62],"satisfies":[65],"discrete":[68],"entropy":[69],"inequalities.":[70],"In":[71],"addition,":[72],"in":[73],"order":[74],"satisfy":[76],"required":[78],"admissibility":[79],"positivity":[85],"both":[87],"density":[89],"and":[90],"pressure":[91],"established.":[93],"Several":[94],"experiments":[96],"attest":[97],"relevance":[99],"developed":[102],"method.":[104],"An":[105],"extension":[106],"two-dimensional":[108],"problems":[109],"given,":[111],"applying":[112],"one-dimensional":[114],"framework":[115],"direction":[116,118],"by":[117],"on":[119],"Cartesian":[120],"grids.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2024-06-21T00:00:00"}