{"id":"https://openalex.org/W4409543029","doi":"https://doi.org/10.1090/mcom/4088","title":"Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: preserving isentropic steady solutions","display_name":"Towards a fully well-balanced and entropy-stable scheme for the Euler equations with gravity: preserving isentropic steady solutions","publication_year":2025,"publication_date":"2025-04-17","ids":{"openalex":"https://openalex.org/W4409543029","doi":"https://doi.org/10.1090/mcom/4088"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4088","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4088","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04620125v2/file/Berthon_Michel-Dansac_Thomann.pdf","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/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"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":true,"raw_author_name":"Christophe Berthon","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Universitd\u0301e Nantes, 2 rue de la Houssinire, BP 92208, 44322 Nantes Cedex 3, France","LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Universitd\u0301e Nantes, 2 rue de la Houssinire, BP 92208, 44322 Nantes Cedex 3, France","institution_ids":["https://openalex.org/I4210153365","https://openalex.org/I1294671590"]},{"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/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I68947357","display_name":"Universit\u00e9 de Strasbourg","ror":"https://ror.org/00pg6eq24","country_code":"FR","type":"education","lineage":["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":"Victor Michel-Dansac","raw_affiliation_strings":["Universit\u00e9 de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France","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)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France","institution_ids":["https://openalex.org/I68947357","https://openalex.org/I1294671590"]},{"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"]}]},{"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/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I68947357","display_name":"Universit\u00e9 de Strasbourg","ror":"https://ror.org/00pg6eq24","country_code":"FR","type":"education","lineage":["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":"Andrea Thomann","raw_affiliation_strings":["Universit\u00e9 de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France","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)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Strasbourg, CNRS, Inria, IRMA, F-67000 Strasbourg, France","institution_ids":["https://openalex.org/I68947357","https://openalex.org/I1294671590"]},{"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103257701"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210153365"],"apc_list":null,"apc_paid":null,"fwci":2.5375,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.86516771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"95","issue":"359","first_page":"1251","last_page":"1292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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":0.9997000098228455,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.996999979019165,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9962000250816345,"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/isentropic-process","display_name":"Isentropic process","score":0.8497586250305176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8029941916465759},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6126942038536072},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.6028217077255249},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.5424604415893555},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.5167926549911499},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5075823068618774},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4427562654018402},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.356122761964798},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.2629261016845703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12419238686561584}],"concepts":[{"id":"https://openalex.org/C172959903","wikidata":"https://www.wikidata.org/wiki/Q907271","display_name":"Isentropic process","level":2,"score":0.8497586250305176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8029941916465759},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6126942038536072},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.6028217077255249},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5424604415893555},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5167926549911499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5075823068618774},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4427562654018402},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.356122761964798},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2629261016845703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12419238686561584}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/4088","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4088","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04620125v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04620125","pdf_url":"https://hal.science/hal-04620125v2/file/Berthon_Michel-Dansac_Thomann.pdf","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2026, 95 (359), pp.1251-1292. ⟨10.1090/mcom/4088⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04620125v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04620125","pdf_url":"https://hal.science/hal-04620125v2/file/Berthon_Michel-Dansac_Thomann.pdf","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2026, 95 (359), pp.1251-1292. ⟨10.1090/mcom/4088⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2715380645","display_name":null,"funder_award_id":"ANR Project MUFFIN ANR-19-CE46-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4415361394","display_name":null,"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/G4648729381","display_name":null,"funder_award_id":"ANR-22-CE25-0017 OptiTrust","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/W4409543029.pdf","grobid_xml":"https://content.openalex.org/works/W4409543029.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W232198546","https://openalex.org/W1968636195","https://openalex.org/W1969760987","https://openalex.org/W1972023531","https://openalex.org/W1975096556","https://openalex.org/W1976632273","https://openalex.org/W1980210033","https://openalex.org/W1988322431","https://openalex.org/W1996468417","https://openalex.org/W2013637933","https://openalex.org/W2019675561","https://openalex.org/W2020752851","https://openalex.org/W2024361440","https://openalex.org/W2031043673","https://openalex.org/W2038157636","https://openalex.org/W2040219002","https://openalex.org/W2043057066","https://openalex.org/W2043798237","https://openalex.org/W2054362419","https://openalex.org/W2060976754","https://openalex.org/W2067678280","https://openalex.org/W2072226973","https://openalex.org/W2073378999","https://openalex.org/W2074900879","https://openalex.org/W2084025336","https://openalex.org/W2086078926","https://openalex.org/W2112548197","https://openalex.org/W2116729868","https://openalex.org/W2142274843","https://openalex.org/W2152122438","https://openalex.org/W2153084536","https://openalex.org/W2155785405","https://openalex.org/W2158288239","https://openalex.org/W2202495949","https://openalex.org/W2221818977","https://openalex.org/W2318625333","https://openalex.org/W2341677735","https://openalex.org/W2394895597","https://openalex.org/W2482838170","https://openalex.org/W2553440700","https://openalex.org/W2604958086","https://openalex.org/W2798758989","https://openalex.org/W2827482115","https://openalex.org/W2830553926","https://openalex.org/W2927725347","https://openalex.org/W2963031533","https://openalex.org/W3002204761","https://openalex.org/W3044652118","https://openalex.org/W3047538078","https://openalex.org/W3100529908","https://openalex.org/W3122532510","https://openalex.org/W3175140547","https://openalex.org/W3176080365","https://openalex.org/W3186583744","https://openalex.org/W3200229483","https://openalex.org/W4205236375","https://openalex.org/W4205791012","https://openalex.org/W4238313514","https://openalex.org/W4386463994","https://openalex.org/W4387929430","https://openalex.org/W4399071955"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2466040413","https://openalex.org/W2009711572","https://openalex.org/W4382053489","https://openalex.org/W2963800366","https://openalex.org/W2365810470","https://openalex.org/W2501406218","https://openalex.org/W1674877062","https://openalex.org/W4394659182","https://openalex.org/W3124634719"],"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-stable":[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":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}