{"id":"https://openalex.org/W7129709025","doi":"https://doi.org/10.48550/arxiv.2602.14392","title":"Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations","display_name":"Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations","publication_year":2026,"publication_date":"2026-02-16","ids":{"openalex":"https://openalex.org/W7129709025","doi":"https://doi.org/10.48550/arxiv.2602.14392"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.14392","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14392","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.14392","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027471730","display_name":"Thomas Izgin","orcid":"https://orcid.org/0000-0003-3235-210X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Izgin, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126249229","display_name":"Andreas Meister","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meister, Andreas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126261611","display_name":"Chi-Wang Shu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shu, Chi-Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001096885","display_name":"Davide Torlo","orcid":"https://orcid.org/0000-0001-5106-1629"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Torlo, Davide","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11416","display_name":"Numerical methods for differential equations","score":0.42579999566078186,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.42579999566078186,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.28139999508857727,"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":0.08150000125169754,"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/euler-equations","display_name":"Euler equations","score":0.7196999788284302},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5756999850273132},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5044000148773193},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.4828000068664551},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.45019999146461487},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.42160001397132874},{"id":"https://openalex.org/keywords/compressible-flow","display_name":"Compressible flow","score":0.41920000314712524},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4133000075817108}],"concepts":[{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.7196999788284302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6570000052452087},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5756999850273132},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5189999938011169},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5044000148773193},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4828000068664551},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.45019999146461487},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.42160001397132874},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.41920000314712524},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4072999954223633},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C2777423268","wikidata":"https://www.wikidata.org/wiki/Q3663116","display_name":"Energy balance","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C2983502797","wikidata":"https://www.wikidata.org/wiki/Q828402","display_name":"Energy density","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.2574999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.14392","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14392","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.14392","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14392","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,"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"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.4950129985809326}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Positivity":[0],"preservation":[1,193],"of":[2,9,22,39,48,52,69,73,95,104,144,194,206,214,223],"key":[3],"physical":[4,31],"quantities":[5,53],"in":[6,66,141,166],"the":[7,28,50,60,67,70,79,85,105,122,126,142,145,164,167,173,181,185,192,204,207,212,220],"context":[8,68,143],"fluid":[10],"flows,":[11],"such":[12],"as":[13,26],"density":[14,86,168],"and":[15,33,62,87,115,150,170],"internal":[16],"energy,":[17],"is":[18,46,59,159,209,217],"an":[19],"essential":[20],"property":[21],"a":[23,35],"numerical":[24,128,175,199],"scheme":[25],"otherwise":[27],"solution":[29],"lacks":[30],"relevance":[32],"has":[34],"not":[36],"well-defined":[37],"equation":[38,169],"state.":[40],"One":[41],"time":[42,56],"integration":[43],"technique":[44],"that":[45,157,203],"capable":[47],"preserving":[49],"positivity":[51],"for":[54],"every":[55,111],"step":[57],"size":[58],"Patankar-trick":[61,80,165],"its":[63],"variants.":[64],"However,":[65],"Euler":[71,147],"equations":[72,90,148],"gas":[74],"dynamics,":[75],"we":[76,100,135],"wonder":[77],"whether":[78],"should":[81],"be":[82],"applied":[83,109],"to":[84,93,110,120,161,171,184,191,201,219],"total":[88],"energy":[89,186],"or":[91],"only":[92,162],"one":[94,102],"them.":[96],"In":[97],"this":[98],"work,":[99],"discuss":[101],"drawback":[103],"schemes":[106,140],"when":[107],"blindly":[108],"positive":[112],"conserved":[113],"variable":[114],"additionally":[116],"point":[117],"out":[118],"how":[119],"overcome":[121],"issue":[123],"by":[124],"balancing":[125],"involved":[127],"fluxes":[129,176],"correctly.":[130],"To":[131],"illustrate":[132],"our":[133,215],"findings,":[134],"investigate":[136],"modified":[137],"Patankar--Runge--Kutta":[138],"(MPRK)":[139],"compressible":[146],"with":[149],"without":[151],"stiff":[152],"source":[153],"terms.":[154],"We":[155,197],"discover":[156],"it":[158],"beneficial":[160],"apply":[163],"balance":[172],"remaining":[174],"consistently":[177],"rather":[178],"than":[179],"applying":[180],"trick":[182],"also":[183,190],"equation.":[187],"This":[188],"leads":[189],"contact":[195],"discontinuities.":[196],"perform":[198],"experiments":[200],"demonstrate":[202],"accuracy":[205],"methods":[208],"maintained":[210],"while":[211],"performance":[213],"approach":[216],"superior":[218],"traditional":[221],"application":[222],"MPRK":[224],"schemes.":[225]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-02-18T00:00:00"}