{"id":"https://openalex.org/W7214770413","doi":"https://doi.org/10.48550/arxiv.2609.34669","title":"Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators","display_name":"Fully Discrete Active Flux Methods for the Euler Equations: Exploring Different Reconstructions and New Multi-Dimensional Evolution Operators","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214770413","doi":"https://doi.org/10.48550/arxiv.2609.34669"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34669","pdf_url":"https://arxiv.org/pdf/2609.34669","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/2609.34669","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071853554","display_name":"Christiane Helzel","orcid":"https://orcid.org/0000-0002-9901-7149","observed_orcids":["https://orcid.org/0000-0002-9901-7149"]},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Helzel, Christiane","raw_affiliation_strings":["Heinrich-Heine-University D\u00fcsseldorf , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Heinrich-Heine-University D\u00fcsseldorf , Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077357327","display_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1","orcid":"https://orcid.org/0000-0002-4351-0161","observed_orcids":["https://orcid.org/0000-0002-4351-0161"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luk\u00e1\u010dov\u00e1-Medvid'ov\u00e1, M\u00e1ria","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120003601","display_name":"Amelie Porfetye","orcid":null,"observed_orcids":[]},"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"]},{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Porfetye, Amelie","raw_affiliation_strings":["Heinrich-Heine-University D\u00fcsseldorf , Germany","Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Heinrich-Heine-University D\u00fcsseldorf , Germany","institution_ids":["https://openalex.org/I44260953"]},{"raw_affiliation_string":"Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026356017","display_name":"Zhuyan Tang","orcid":null,"observed_orcids":[]},"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":"Tang, Zhuyan","raw_affiliation_strings":["Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9980000257492065,"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":0.9980000257492065,"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":0.001500000013038516,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/euler-equations","display_name":"Euler equations","score":0.9319999814033508},{"id":"https://openalex.org/keywords/gas-dynamics","display_name":"gas dynamics","score":0.9909999966621399},{"id":"https://openalex.org/keywords/bicharacteristics","display_name":"bicharacteristics","score":0.8870000243186951},{"id":"https://openalex.org/keywords/third-order-accuracy","display_name":"third-order accuracy","score":0.9129999876022339},{"id":"https://openalex.org/keywords/stability","display_name":"stability","score":0.5009999871253967},{"id":"https://openalex.org/keywords/accuracy","display_name":"accuracy","score":0.3179999887943268},{"id":"https://openalex.org/keywords/cartesian-grid-method","display_name":"Cartesian grid method","score":0.6240000128746033}],"concepts":[{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6696000099182129},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6377999782562256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6015999913215637},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.5461000204086304},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5320000052452087},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5069000124931335},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5012000203132629},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.498199999332428},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.4235000014305115},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.40369999408721924},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C158457486","wikidata":"https://www.wikidata.org/wiki/Q17104301","display_name":"Multidimensional systems","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C48330753","wikidata":"https://www.wikidata.org/wiki/Q374926","display_name":"Euler summation","level":5,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34669","pdf_url":"https://arxiv.org/pdf/2609.34669","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.2609.34669","doi":"https://doi.org/10.48550/arxiv.2609.34669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34669","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.34669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34669","pdf_url":"https://arxiv.org/pdf/2609.34669","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/G1709802964","display_name":"Zuf\u00e4llige kompressible Euler Gleichungen: Numerik und ihre Analysis","funder_award_id":"525853336","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/G5575399030","display_name":"Active Flux Verfahren f\u00fcr die Euler Gleichungen","funder_award_id":"525800857","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214770413.pdf","grobid_xml":"https://content.openalex.org/works/W7214770413.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W7117131871","https://openalex.org/W7125792731","https://openalex.org/W7161179871","https://openalex.org/W7165622439","https://openalex.org/W7171742309"],"related_works":["https://openalex.org/W4415193778","https://openalex.org/W7165622439","https://openalex.org/W4387323752","https://openalex.org/W4415889927","https://openalex.org/W4417530157","https://openalex.org/W7161179871","https://openalex.org/W4392375572","https://openalex.org/W3104143153","https://openalex.org/W4387225028","https://openalex.org/W6989834578"],"abstract_inverted_index":{"We":[0,58],"present":[1],"new":[2],"fully":[3],"discrete":[4],"Cartesian":[5],"grid":[6],"Active":[7],"Flux":[8],"methods":[9,23],"for":[10,45],"the":[11,25,49,54,62,71,76],"two-dimensional":[12],"Euler":[13,51],"equations":[14,52],"of":[15,21,33,48,56,66,75],"gas":[16],"dynamics.":[17],"A":[18],"key":[19],"component":[20],"these":[22],"is":[24],"evolution":[26,43,68],"operator":[27,69],"used":[28],"to":[29],"evolve":[30],"point-value":[31,46],"degrees":[32],"freedom.":[34],"Therefore,":[35],"we":[36],"derive":[37],"several":[38],"new,":[39],"third-order":[40],"accurate,":[41],"multidimensional":[42],"operators":[44],"updates":[47],"linearized":[50],"using":[53],"method":[55],"bicharacteristics.":[57],"also":[59],"investigate":[60],"how":[61],"reconstruction":[63],"and":[64,73],"choice":[65],"approximate":[67],"affect":[70],"accuracy":[72],"stability":[74],"resulting":[77],"methods.":[78]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}