{"id":"https://openalex.org/W2046926864","doi":"https://doi.org/10.1137/090752821","title":"Adaptive Timestep Control for Nonstationary Solutions of the Euler Equations","display_name":"Adaptive Timestep Control for Nonstationary Solutions of the Euler Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2046926864","doi":"https://doi.org/10.1137/090752821","mag":"2046926864"},"language":"en","primary_location":{"id":"doi:10.1137/090752821","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752821","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087427983","display_name":"Christina Steiner","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christina Steiner","raw_affiliation_strings":["steiner@igpm.rwth-aachen.de and mueller@igpm.rwth-aachen.de and noelle@igpm.rwth-aachen.de#TAB#"],"affiliations":[{"raw_affiliation_string":"steiner@igpm.rwth-aachen.de and mueller@igpm.rwth-aachen.de and noelle@igpm.rwth-aachen.de#TAB#","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112063217","display_name":"Siegfried M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Siegfried M\u00fcller","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen University, D-Templergraben 55, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen University, D-Templergraben 55, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025832688","display_name":"Sebastian Noelle","orcid":"https://orcid.org/0000-0001-6267-8309"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Noelle","raw_affiliation_strings":["Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen University, D-Templergraben 55, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen University, D-Templergraben 55, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087427983"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.3443,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62264996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"32","issue":"3","first_page":"1617","last_page":"1651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.9994000196456909,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976999759674072,"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/conservation-law","display_name":"Conservation law","score":0.7530369758605957},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6350712776184082},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6289348006248474},{"id":"https://openalex.org/keywords/inviscid-flow","display_name":"Inviscid flow","score":0.5729409456253052},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5333157777786255},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5286928415298462},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5238915681838989},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4582177698612213},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.45349252223968506},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4530453681945801},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4216425120830536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3068235218524933},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2727925479412079},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17561593651771545},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13481688499450684}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7530369758605957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6350712776184082},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6289348006248474},{"id":"https://openalex.org/C86252789","wikidata":"https://www.wikidata.org/wiki/Q2247765","display_name":"Inviscid flow","level":2,"score":0.5729409456253052},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5333157777786255},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5286928415298462},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5238915681838989},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4582177698612213},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.45349252223968506},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4530453681945801},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4216425120830536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3068235218524933},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2727925479412079},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17561593651771545},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13481688499450684},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090752821","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752821","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G1655496666","display_name":null,"funder_award_id":"SFB 401","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"},{"id":"https://openalex.org/F4320324232","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1970850839","https://openalex.org/W2012164750","https://openalex.org/W2015407979","https://openalex.org/W2029859487","https://openalex.org/W2032576984","https://openalex.org/W2040476229","https://openalex.org/W2042118059","https://openalex.org/W2042940420","https://openalex.org/W2044084385","https://openalex.org/W2046899724","https://openalex.org/W2047554497","https://openalex.org/W2048270347","https://openalex.org/W2050051055","https://openalex.org/W2060732875","https://openalex.org/W2069050972","https://openalex.org/W2080049628","https://openalex.org/W2121296933","https://openalex.org/W2131918275","https://openalex.org/W2140153041","https://openalex.org/W2962793647","https://openalex.org/W3005363104","https://openalex.org/W4243839716","https://openalex.org/W4245037559","https://openalex.org/W4292169137","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W2933342328","https://openalex.org/W2024551412","https://openalex.org/W2029877474","https://openalex.org/W4300105121","https://openalex.org/W2936887813","https://openalex.org/W2963315378","https://openalex.org/W4226163825","https://openalex.org/W4391013527","https://openalex.org/W4379538724","https://openalex.org/W3211383997"],"abstract_inverted_index":{"In":[0],"this":[1,173],"paper":[2],"we":[3,147,171],"continue":[4],"our":[5],"work":[6],"on":[7],"adaptive":[8,138,182],"timestep":[9,198],"control":[10],"for":[11,43,55,72,124,158,190],"weakly":[12,194],"nonstationary":[13,195],"problems":[14],"[C.":[15],"Steiner":[16],"and":[17,53,70,86,132,170,209],"S.":[18],"Noelle,":[19],"Internat.":[20],"J.":[21],"Numer.":[22],"Methods":[23],"Biomedical":[24],"Engrg.,":[25],"26":[26],"(2010),":[27],"pp.":[28,84],"790\u2013806].":[29],"The":[30,95,179,197,219],"core":[31],"of":[32,39,59,115,121,128,136,188,193,206,221,228],"the":[33,101,110,119,129,134,137,144,216,222],"method":[34,183],"is":[35,224],"a":[36,125,149,213,235],"space-time":[37,181],"splitting":[38],"adjoint":[40,130],"error":[41,51],"representations":[42],"target":[44],"functionals":[45],"due":[46],"to":[47,65,109],"S\u00fcli":[48],"[A":[49],"posteriori":[50],"analysis":[52],"adaptivity":[54],"finite":[56],"element":[57],"approximations":[58],"hyperbolic":[60],"problems,":[61],"in":[62,68,203],"An":[63],"Introduction":[64],"Recent":[66],"Developments":[67],"Theory":[69],"Numerics":[71],"Conservation":[73,159],"Laws,":[74,160],"Lect.":[75,161],"Notes":[76,162],"Comput.":[77,163],"Sci.":[78,164],"Eng.":[79,165],"5,":[80],"Springer,":[81,167],"Berlin,":[82,168],"1999,":[83],"123\u2013194]":[85],"Hartmann":[87],"[Master's":[88],"thesis,":[89],"Universit\u00e4t":[90],"Heidelberg,":[91,92],"Germany,":[93],"1998].":[94],"main":[96],"new":[97,126],"ingredients":[98],"are":[99],"(i)":[100],"extension":[102],"from":[103],"scalar,":[104],"one-dimensional":[105],"(1D),":[106],"conservation":[107],"laws":[108],"two-dimensional":[111],"(2D)":[112],"Euler":[113],"equations":[114],"gas":[116],"dynamics,":[117],"(ii)":[118],"derivation":[120],"boundary":[122],"conditions":[123],"formulation":[127],"problem,":[131],"(iii)":[133],"coupling":[135],"time-stepping":[139],"with":[140,174],"spatial":[141,145],"adaptation.":[142],"For":[143],"adaptation,":[146],"use":[148],"multiresolution-based":[150],"strategy":[151],"developed":[152],"by":[153,226],"M\u00fcller":[154],"[Adaptive":[155],"Multiscale":[156],"Schemes":[157],"27,":[166],"2003],":[169],"combine":[172],"an":[175,185,229],"implicit":[176,191],"time":[177,204],"discretization.":[178],"combined":[180],"provides":[184],"efficient":[186],"choice":[187],"timesteps":[189],"computations":[192],"flows.":[196],"will":[199],"be":[200],"very":[201],"large":[202],"intervals":[205],"stationary":[207],"flow":[208,217,233],"becomes":[210],"small":[211],"when":[212],"perturbation":[214],"enters":[215],"field.":[218],"efficiency":[220],"solver":[223],"investigated":[225],"means":[227],"unsteady":[230],"inviscid":[231],"2D":[232],"over":[234],"bump.":[236]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
