{"id":"https://openalex.org/W7220735564","doi":"https://doi.org/10.48550/arxiv.2610.05820","title":"Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form","display_name":"Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220735564","doi":"https://doi.org/10.48550/arxiv.2610.05820"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05820","pdf_url":"https://arxiv.org/pdf/2610.05820","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,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.05820","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107619836","display_name":"Marco Artiano","orcid":"https://orcid.org/0009-0009-5872-702X","observed_orcids":["https://orcid.org/0009-0009-5872-702X"]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Artiano, Marco","raw_affiliation_strings":["Institute of Mathematics , Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026754409","display_name":"Kieran Ricardo","orcid":"https://orcid.org/0009-0000-4544-3049","observed_orcids":["https://orcid.org/0009-0000-4544-3049"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricardo, Kieran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034928986","display_name":"Oswald Knoth","orcid":"https://orcid.org/0000-0002-1003-3207","observed_orcids":["https://orcid.org/0000-0002-1003-3207"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Knoth, Oswald","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017730275","display_name":"Peter Spichtinger","orcid":"https://orcid.org/0000-0003-4008-4977","observed_orcids":["https://orcid.org/0000-0003-4008-4977"]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Spichtinger, Peter","raw_affiliation_strings":["Institute for Atmospheric Physics , Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Atmospheric Physics , Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056123559","display_name":"Hendrik Ranocha","orcid":"https://orcid.org/0000-0002-3456-2277","observed_orcids":["https://orcid.org/0000-0002-3456-2277"]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ranocha, Hendrik","raw_affiliation_strings":["Institute of Mathematics , Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9663000106811523,"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":0.9663000106811523,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.032600000500679016,"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy-stable-schemes","display_name":"entropy stable schemes","score":0.7440000176429749},{"id":"https://openalex.org/keywords/well-balanced-schemes","display_name":"well-balanced schemes","score":0.9800000190734863},{"id":"https://openalex.org/keywords/discontinuous-galerkin-spectral-element-method","display_name":"discontinuous Galerkin spectral element method","score":0.9229999780654907},{"id":"https://openalex.org/keywords/compressible-euler-equations","display_name":"compressible Euler equations","score":0.9909999966621399},{"id":"https://openalex.org/keywords/potential-temperature","display_name":"potential temperature","score":0.8999999761581421},{"id":"https://openalex.org/keywords/entropy-conservation","display_name":"entropy conservation","score":0.546999990940094},{"id":"https://openalex.org/keywords/conservation-of-energy","display_name":"conservation of energy","score":0.8790000081062317},{"id":"https://openalex.org/keywords/numerical-flux","display_name":"numerical flux","score":0.6209999918937683},{"id":"https://openalex.org/keywords/curvilinear-meshes","display_name":"curvilinear meshes","score":0.7710000276565552},{"id":"https://openalex.org/keywords/atmospheric-dynamical-core","display_name":"atmospheric dynamical core","score":0.8109999895095825},{"id":"https://openalex.org/keywords/gravity","display_name":"gravity","score":0.8029999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6388999819755554},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.6126999855041504},{"id":"https://openalex.org/C172959903","wikidata":"https://www.wikidata.org/wiki/Q907271","display_name":"Isentropic process","level":2,"score":0.6061000227928162},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5685999989509583},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5483999848365784},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5374000072479248},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5321000218391418},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5170999765396118},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.44690001010894775},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3799999952316284},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.37630000710487366},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.361299991607666},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.357699990272522},{"id":"https://openalex.org/C133347239","wikidata":"https://www.wikidata.org/wiki/Q486921","display_name":"Isothermal process","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C134853933","wikidata":"https://www.wikidata.org/wiki/Q208641","display_name":"Hydrostatic equilibrium","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C159188206","wikidata":"https://www.wikidata.org/wiki/Q1478382","display_name":"Heat flux","level":3,"score":0.30149999260902405},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.29580000042915344},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.2702000141143799},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26570001244544983},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2506999969482422},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05820","pdf_url":"https://arxiv.org/pdf/2610.05820","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,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.05820","doi":"https://doi.org/10.48550/arxiv.2610.05820","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05820","pdf_url":null,"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,"listed_in":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.05820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05820","pdf_url":"https://arxiv.org/pdf/2610.05820","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,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G165440837","display_name":"EsCUT: Entropystabile h\u00f6hereOrdnung CUTcell discontinuous Galerkin Verfahren","funder_award_id":"526031774","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3044548687","display_name":null,"funder_award_id":"SPP 2410","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5545999061","display_name":"Zug\u00e4ngliches H\u00f6chstleistungsrechnen mit Trixi.jl und der Programmiersprache Julia","funder_award_id":"528753982","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220735564.pdf","grobid_xml":"https://content.openalex.org/works/W7220735564.grobid-xml"},"referenced_works_count":80,"referenced_works":["https://openalex.org/W57092545","https://openalex.org/W232198546","https://openalex.org/W767107293","https://openalex.org/W1486816047","https://openalex.org/W1823032471","https://openalex.org/W1908859542","https://openalex.org/W1971879059","https://openalex.org/W1976632273","https://openalex.org/W1983165369","https://openalex.org/W1988497189","https://openalex.org/W1990596161","https://openalex.org/W1998887941","https://openalex.org/W2008046188","https://openalex.org/W2010222530","https://openalex.org/W2038408857","https://openalex.org/W2041983391","https://openalex.org/W2049068370","https://openalex.org/W2053715298","https://openalex.org/W2053810476","https://openalex.org/W2060718211","https://openalex.org/W2064390862","https://openalex.org/W2066734144","https://openalex.org/W2072226973","https://openalex.org/W2078033075","https://openalex.org/W2100103443","https://openalex.org/W2120575449","https://openalex.org/W2142212336","https://openalex.org/W2143332803","https://openalex.org/W2150128292","https://openalex.org/W2169202988","https://openalex.org/W2219241263","https://openalex.org/W2283777036","https://openalex.org/W2319470458","https://openalex.org/W2343405662","https://openalex.org/W2470872792","https://openalex.org/W2545221020","https://openalex.org/W2560240534","https://openalex.org/W2605493455","https://openalex.org/W2618630098","https://openalex.org/W2619381903","https://openalex.org/W2768455612","https://openalex.org/W2772909518","https://openalex.org/W2791413969","https://openalex.org/W2806863959","https://openalex.org/W2810690184","https://openalex.org/W2810842845","https://openalex.org/W2949414414","https://openalex.org/W2956078903","https://openalex.org/W2985723910","https://openalex.org/W2997129356","https://openalex.org/W3012383019","https://openalex.org/W3021138559","https://openalex.org/W3080513263","https://openalex.org/W3095098477","https://openalex.org/W3116091955","https://openalex.org/W3189626104","https://openalex.org/W3195221648","https://openalex.org/W3198332808","https://openalex.org/W3201132461","https://openalex.org/W4224102766","https://openalex.org/W4289342468","https://openalex.org/W4294591104","https://openalex.org/W4321350219","https://openalex.org/W4366832513","https://openalex.org/W4387101632","https://openalex.org/W4400648340","https://openalex.org/W4403969957","https://openalex.org/W4404405962","https://openalex.org/W4405267446","https://openalex.org/W4407259750","https://openalex.org/W4410461541","https://openalex.org/W4416203788","https://openalex.org/W7134165301","https://openalex.org/W7139919524","https://openalex.org/W7161716186","https://openalex.org/W7171647958","https://openalex.org/W7171838603","https://openalex.org/W7171977404","https://openalex.org/W7202147183","https://openalex.org/W7219801123"],"related_works":["https://openalex.org/W3210200204","https://openalex.org/W4289342468","https://openalex.org/W4414746962","https://openalex.org/W2912217407","https://openalex.org/W2885327292","https://openalex.org/W3145216770","https://openalex.org/W4382706111","https://openalex.org/W3206676988","https://openalex.org/W7131255112","https://openalex.org/W4394807144"],"abstract_inverted_index":{"We":[0],"develop":[1],"structure-preserving":[2],"methods":[3],"for":[4,66,104,110],"the":[5,22,33,49,53,81,92,97,102],"compressible":[6],"Euler":[7],"equations":[8],"with":[9],"gravity":[10],"in":[11,106],"vector-invariant":[12],"form":[13],"and":[14,38,52,69,95,99],"potential":[15],"temperature":[16],"as":[17,36],"a":[18],"prognostic":[19],"variable":[20],"within":[21],"flux-differencing":[23],"discontinuous":[24],"Galerkin":[25],"spectral":[26],"element":[27],"method":[28],"(DGSEM)":[29],"framework.":[30],"By":[31],"discretizing":[32],"nonconservative":[34],"terms":[35],"symmetric":[37],"antisymmetric":[39],"products,":[40],"we":[41,57],"derive":[42],"two-point":[43],"numerical":[44,61,89],"fluxes":[45],"that":[46,63],"conserve":[47],"both":[48,67],"thermodynamic":[50],"entropy":[51],"total":[54],"energy.":[55],"Moreover,":[56],"design":[58],"an":[59],"entropy-stable":[60],"flux":[62],"is":[64],"well-balanced":[65],"isothermal":[68],"isentropic":[70],"background":[71],"states.":[72],"All":[73],"properties":[74],"are":[75],"shown":[76],"to":[77,80],"carry":[78],"over":[79],"high-order":[82],"DGSEM":[83],"on":[84],"general":[85],"curvilinear":[86],"meshes.":[87],"Several":[88],"examples":[90],"confirm":[91],"theoretical":[93],"findings":[94],"show":[96],"robustness":[98],"accuracy":[100],"of":[101],"scheme":[103],"use":[105],"modern":[107],"dynamical":[108],"cores":[109],"atmospheric":[111],"flows.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}