{"id":"https://openalex.org/W2090617571","doi":"https://doi.org/10.1137/040607460","title":"Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section","display_name":"Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2090617571","doi":"https://doi.org/10.1137/040607460","mag":"2090617571"},"language":"en","primary_location":{"id":"doi:10.1137/040607460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607460","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5112232900","display_name":"Dietmar Kr\u00f6ner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dietmar Kr\u00f6ner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081889508","display_name":"Mai Duc Thanh","orcid":"https://orcid.org/0000-0002-9532-3683"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mai Duc Thanh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1245,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.86688784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"796","last_page":"824"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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":0.9994999766349792,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7140181064605713},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6667362451553345},{"id":"https://openalex.org/keywords/compressible-flow","display_name":"Compressible flow","score":0.6017366051673889},{"id":"https://openalex.org/keywords/nozzle","display_name":"Nozzle","score":0.5558715462684631},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5434655547142029},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5248082876205444},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42493346333503723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4194833040237427},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41056889295578003},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4020387828350067},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.33251315355300903},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.296980082988739},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17682325839996338}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7140181064605713},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6667362451553345},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.6017366051673889},{"id":"https://openalex.org/C56200935","wikidata":"https://www.wikidata.org/wiki/Q250840","display_name":"Nozzle","level":2,"score":0.5558715462684631},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5434655547142029},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5248082876205444},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42493346333503723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4194833040237427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41056889295578003},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4020387828350067},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.33251315355300903},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.296980082988739},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17682325839996338},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040607460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607460","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:62076","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/62076","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis. - 43, 2 (2005) , 796-824, ISSN: 0036-1429","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W348217116","https://openalex.org/W1509181904","https://openalex.org/W1554134448","https://openalex.org/W1595775464","https://openalex.org/W1975628738","https://openalex.org/W1984405076","https://openalex.org/W1993392273","https://openalex.org/W2000040540","https://openalex.org/W2008068453","https://openalex.org/W2024247620","https://openalex.org/W2028172847","https://openalex.org/W2039594536","https://openalex.org/W2051740894","https://openalex.org/W2073378999","https://openalex.org/W2075776956","https://openalex.org/W2084025336","https://openalex.org/W2085844395","https://openalex.org/W2101584042","https://openalex.org/W2125266650","https://openalex.org/W2155785405","https://openalex.org/W2254772253","https://openalex.org/W2329976704","https://openalex.org/W2482838170","https://openalex.org/W4205317898"],"related_works":["https://openalex.org/W2914126368","https://openalex.org/W2039262714","https://openalex.org/W4238997598","https://openalex.org/W4247269991","https://openalex.org/W120161679","https://openalex.org/W2049521192","https://openalex.org/W2188135746","https://openalex.org/W244130144","https://openalex.org/W2967266163","https://openalex.org/W2046242099"],"abstract_inverted_index":{"Compressible":[0],"flows":[1],"in":[2,13,105],"a":[3,49],"nozzle":[4],"can":[5],"be":[6,66],"modeled":[7],"by":[8],"the":[9,26,33,38,56,74,77,90,93,102],"gas":[10],"dynamics":[11],"equations":[12],"one-dimensional":[14],"space":[15],"with":[16],"source":[17],"terms.":[18],"It":[19],"turns":[20],"out":[21],"that":[22],"along":[23],"stationary":[24,41,59],"waves,":[25],"entropy":[27],"is":[28,63],"conserved.":[29],"Investigating":[30],"properties":[31],"of":[32,40,58,68,76,92],"system":[34],"leads":[35],"us":[36],"to":[37,65],"determination":[39],"waves.":[42,60],"Relying":[43],"on":[44],"this":[45],"analysis,":[46],"we":[47],"construct":[48],"numerical":[50],"scheme":[51,62,79,97],"which":[52,83],"takes":[53],"into":[54],"account":[55],"use":[57],"Our":[61],"shown":[64],"capable":[67],"maintaining":[69],"equilibrium":[70],"states.":[71],"This":[72],"demonstrates":[73],"efficiency":[75],"new":[78],"over":[80],"classical":[81,103],"ones,":[82],"usually":[84],"give":[85],"unsatisfactory":[86],"results":[87],"when":[88],"reducing":[89],"refinement":[91],"mesh-size.":[94],"Moreover,":[95],"our":[96],"converges":[98],"much":[99],"faster":[100],"than":[101],"ones":[104],"most":[106],"cases.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}