{"id":"https://openalex.org/W2945076242","doi":"https://doi.org/10.1137/19m1263480","title":"Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations","display_name":"Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2945076242","doi":"https://doi.org/10.1137/19m1263480","mag":"2945076242"},"language":"en","primary_location":{"id":"doi:10.1137/19m1263480","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263480","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.09129","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hendrik Ranocha","orcid":"https://orcid.org/0000-0002-3456-2277"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hendrik Ranocha","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3456-2277","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Mohammed Sayyari","orcid":"https://orcid.org/0000-0003-4967-501X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammed Sayyari","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4967-501X","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Lisandro Dalcin","orcid":"https://orcid.org/0000-0001-8086-0155"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lisandro Dalcin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8086-0155","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Matteo Parsani","orcid":"https://orcid.org/0000-0001-7300-1280"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matteo Parsani","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7300-1280","affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"David I. Ketcheson","orcid":"https://orcid.org/0000-0002-1212-126X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David I. Ketcheson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1212-126X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":20.9789,"has_fulltext":false,"cited_by_count":129,"citation_normalized_percentile":{"value":0.99884206,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"42","issue":"2","first_page":"A612","last_page":"A638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.3653999865055084,"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":0.3653999865055084,"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":0.24969999492168427,"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":0.2401999980211258,"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/scalar","display_name":"Scalar (mathematics)","score":0.5640000104904175},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5467000007629395},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5246999859809875},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.48420000076293945},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.4837000072002411},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4505000114440918},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.44670000672340393},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4440999925136566},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4223000109195709}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7922000288963318},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5640000104904175},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5619999766349792},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4837000072002411},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4505000114440918},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.42080000042915344},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.400299996137619},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3467000126838684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34619998931884766},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3398999869823456},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.3179999887943268},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.31279999017715454},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2590000033378601},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2533999979496002}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1263480","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263480","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.09129","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.09129","pdf_url":"https://arxiv.org/pdf/1905.09129","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/659959","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/659959","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/662142","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/662142","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.09129","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.09129","pdf_url":"https://arxiv.org/pdf/1905.09129","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1976314836","https://openalex.org/W1981017638","https://openalex.org/W1984432912","https://openalex.org/W1990596161","https://openalex.org/W1995213327","https://openalex.org/W2010222530","https://openalex.org/W2019720983","https://openalex.org/W2049835313","https://openalex.org/W2049888254","https://openalex.org/W2064163434","https://openalex.org/W2064265035","https://openalex.org/W2072226973","https://openalex.org/W2081057745","https://openalex.org/W2085471512","https://openalex.org/W2123457528","https://openalex.org/W2123809583","https://openalex.org/W2124874924","https://openalex.org/W2138746820","https://openalex.org/W2142212336","https://openalex.org/W2146188963","https://openalex.org/W2157563040","https://openalex.org/W2167278920","https://openalex.org/W2177309472","https://openalex.org/W2273401166","https://openalex.org/W2329372382","https://openalex.org/W2526384912","https://openalex.org/W2529409243","https://openalex.org/W2743040688","https://openalex.org/W2765460213","https://openalex.org/W2771999305","https://openalex.org/W2794024391","https://openalex.org/W2888114187","https://openalex.org/W2902420577","https://openalex.org/W2964350974","https://openalex.org/W2995756203","https://openalex.org/W3010292040"],"related_works":[],"abstract_inverted_index":{"The":[0,75,96,119],"framework":[1],"of":[2,44,105,121],"inner":[3],"product":[4],"norm":[5],"preserving":[6],"relaxation":[7,46],"Runge--Kutta":[8,51,85],"methods":[9,86],"[D.":[10],"I.":[11],"Ketcheson,":[12],"SIAM":[13],"J.":[14],"Numer.":[15],"Anal.,":[16],"57":[17],"(2019),":[18],"pp.":[19],"2850--2870]":[20],"is":[21,102,117,124],"extended":[22],"to":[23,35,80,93,135],"general":[24],"convex":[25,37],"quantities.":[26],"Conservation,":[27],"dissipation,":[28],"or":[29],"other":[30,57],"solution":[31,104],"properties":[32,72],"with":[33],"respect":[34],"any":[36],"functional":[38],"are":[39,73],"enforced":[40],"by":[41],"the":[42,50,103,146],"addition":[43],"a":[45,90,113],"parameter":[47],"that":[48],"multiplies":[49],"update":[52],"at":[53,99],"each":[54,100],"step.":[55],"Moreover,":[56],"desirable":[58],"stability":[59,63],"(such":[60,67],"as":[61,68],"strong":[62],"preservation)":[64],"and":[65,83,87,127,139,149],"efficiency":[66],"low":[69],"storage":[70],"requirements)":[71],"preserved.":[74],"technique":[76],"can":[77],"be":[78],"applied":[79],"both":[81],"explicit":[82],"implicit":[84],"requires":[88],"only":[89],"small":[91],"modification":[92],"existing":[94],"implementations.":[95],"computational":[97],"cost":[98],"step":[101],"one":[106],"additional":[107],"scalar":[108],"algebraic":[109],"equation":[110],"for":[111,145],"which":[112],"good":[114],"initial":[115],"guess":[116],"available.":[118],"effectiveness":[120],"this":[122],"approach":[123],"proved":[125],"analytically":[126],"demonstrated":[128],"in":[129],"several":[130],"numerical":[131],"examples,":[132],"including":[133],"applications":[134],"high":[136],"order":[137],"entropy-conservative":[138],"entropy-stable":[140],"semidiscretizations":[141],"on":[142],"unstructured":[143],"grids":[144],"compressible":[147],"Euler":[148],"Navier--Stokes":[150],"equations.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":30},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":12}],"updated_date":"2026-05-13T08:25:38.343686","created_date":"2019-05-29T00:00:00"}
