{"id":"https://openalex.org/W2010881476","doi":"https://doi.org/10.1137/0914011","title":"An<i>h</i>-<i>r</i>-Adaptive Approximate Riemann Solver for the Euler Equations in Two Dimensions","display_name":"An<i>h</i>-<i>r</i>-Adaptive Approximate Riemann Solver for the Euler Equations in Two Dimensions","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2010881476","doi":"https://doi.org/10.1137/0914011","mag":"2010881476"},"language":"en","primary_location":{"id":"doi:10.1137/0914011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914011","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/A5039120348","display_name":"Michael G. Edwards","orcid":"https://orcid.org/0000-0003-2948-4101"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael G. Edwards","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038134825","display_name":"J. Tinsley Oden","orcid":"https://orcid.org/0000-0001-9973-9566"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Tinsley Oden","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082045365","display_name":"Leszek Demkowicz","orcid":"https://orcid.org/0000-0001-7839-8037"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leszek Demkowicz","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039120348"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5533,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87829369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"1","first_page":"185","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.998199999332428,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9970999956130981,"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/mathematics","display_name":"Mathematics","score":0.8724126815795898},{"id":"https://openalex.org/keywords/riemann-solver","display_name":"Riemann solver","score":0.7978627681732178},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.7272594571113586},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.6939033269882202},{"id":"https://openalex.org/keywords/roe-solver","display_name":"Roe solver","score":0.6180791854858398},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.5839537978172302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.579735517501831},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.5627395510673523},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.502112627029419},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5019996166229248},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.4879416823387146},{"id":"https://openalex.org/keywords/compressible-flow","display_name":"Compressible flow","score":0.48038703203201294},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4487093389034271},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43305543065071106},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42545440793037415},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.40931233763694763},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.20332154631614685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13815993070602417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13582459092140198}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8724126815795898},{"id":"https://openalex.org/C120796332","wikidata":"https://www.wikidata.org/wiki/Q6153788","display_name":"Riemann solver","level":3,"score":0.7978627681732178},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.7272594571113586},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.6939033269882202},{"id":"https://openalex.org/C171520575","wikidata":"https://www.wikidata.org/wiki/Q7357538","display_name":"Roe solver","level":4,"score":0.6180791854858398},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5839537978172302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.579735517501831},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5627395510673523},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.502112627029419},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5019996166229248},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4879416823387146},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.48038703203201294},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4487093389034271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43305543065071106},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42545440793037415},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.40931233763694763},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.20332154631614685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13815993070602417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13582459092140198},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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:10.1137/0914011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914011","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1532515344","https://openalex.org/W1975706278","https://openalex.org/W1990340775","https://openalex.org/W1998602489","https://openalex.org/W1998830482","https://openalex.org/W1999399767","https://openalex.org/W2000583527","https://openalex.org/W2003047049","https://openalex.org/W2031171101","https://openalex.org/W2031674418","https://openalex.org/W2049161806","https://openalex.org/W2053452001","https://openalex.org/W2058221859","https://openalex.org/W2059102113","https://openalex.org/W2060161546","https://openalex.org/W2075598188","https://openalex.org/W2586324090","https://openalex.org/W4245037559","https://openalex.org/W4248625248","https://openalex.org/W4292169137","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W2074800504","https://openalex.org/W2326925276","https://openalex.org/W1577037560","https://openalex.org/W1663225052","https://openalex.org/W2010276774","https://openalex.org/W2010881476","https://openalex.org/W2922234216","https://openalex.org/W2082097634","https://openalex.org/W2183053070","https://openalex.org/W2074900879"],"abstract_inverted_index":{"A":[0,78],"new":[1],"adaptive":[2,111,118],"strategy":[3],"for":[4,30,86],"solving":[5],"the":[6,39,66,69,73,95,100,103],"Euler":[7],"equations":[8],"of":[9,16,44,52,68,72,94],"compressible":[10],"flow":[11],"is":[12,25,36,62,84,107],"presented.":[13],"The":[14,117],"method":[15,74],"Roe":[17],"[J.":[18],"Comput.":[19],"Phys.,":[20],"43":[21],"(1981),":[22],"pp.":[23],"357\u2013372]":[24],"extended":[26],"into":[27,75],"two":[28,76],"dimensions":[29],"an":[31,92],"arbitrary":[32],"quadrilateral":[33,41,54],"grid":[34,55,59],"and":[35,46,110,115,127],"coupled":[37],"with":[38,91],"h-adaptive":[40],"refinement-unrefinement":[42],"algorithm":[43],"Demkowicz":[45],"Oden":[47],"[TICOM":[48],"Report":[49],"88-02].":[50],"Refinement":[51],"a":[53,57,87],"retains":[56],"certain":[58],"structure":[60],"which":[61],"fully":[63],"exploited":[64],"by":[65,99],"extension":[67],"higher-order":[70],"version":[71],"dimensions.":[77],"total":[79],"variation":[80],"diminishing":[81],"(TVD)":[82],"analysis":[83],"presented":[85],"nonuniform":[88],"grid,":[89],"together":[90],"assessment":[93],"solution":[96],"error":[97],"induced":[98],"nonuniformity":[101],"in":[102,130],"grid.":[104],"Grid":[105],"movement":[106],"also":[108],"considered":[109],"strategies":[112],"are":[113,133],"discussed":[114],"tested.":[116],"scheme":[119],"proves":[120],"to":[121],"be":[122],"highly":[123],"robust.":[124],"Improved":[125],"accuracy":[126],"large":[128],"savings":[129],"computer":[131],"time":[132],"obtained.":[134]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}