{"id":"https://openalex.org/W2094227152","doi":"https://doi.org/10.1115/fedsm2013-16378","title":"Implications of Using Dual Number Derivatives With a Numerical Solution","display_name":"Implications of Using Dual Number Derivatives With a Numerical Solution","publication_year":2013,"publication_date":"2013-07-07","ids":{"openalex":"https://openalex.org/W2094227152","doi":"https://doi.org/10.1115/fedsm2013-16378","mag":"2094227152"},"language":"en","primary_location":{"id":"doi:10.1115/fedsm2013-16378","doi":"https://doi.org/10.1115/fedsm2013-16378","is_oa":false,"landing_page_url":"https://doi.org/10.1115/fedsm2013-16378","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Volume 1A, Symposia: Advances in Fluids Engineering Education; Advances in Numerical Modeling for Turbomachinery Flow Optimization; Applications in CFD; Bio-Inspired Fluid Mechanics; CFD Verification and Validation; Development and Applications of Immersed Boundary Methods; DNS, LES, and Hybrid RANS/LES Methods","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","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/A5059979461","display_name":"Suryanarayana Raju Pakalapati","orcid":"https://orcid.org/0000-0001-8571-4958","observed_orcids":["https://orcid.org/0000-0001-8571-4958"]},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Suryanarayana R. Pakalapati","raw_affiliation_strings":["West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103529803","display_name":"Hayri Sezer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hayri Sezer","raw_affiliation_strings":["West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019452130","display_name":"Ismail Bektas Celik","orcid":"https://orcid.org/0000-0002-4726-1238","observed_orcids":["https://orcid.org/0000-0002-4726-1238"]},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ismail B. Celik","raw_affiliation_strings":["West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I12097938"],"apc_list":null,"apc_paid":null,"fwci":0.9953,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74018862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.44530001282691956,"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":0.44530001282691956,"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":0.18250000476837158,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.09470000118017197,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"automatic differentiation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.9610000252723694},{"id":"https://openalex.org/keywords/parameter-sensitivity","display_name":"parameter sensitivity","score":0.7879999876022339},{"id":"https://openalex.org/keywords/numerical-uncertainty","display_name":"numerical uncertainty","score":0.6919999718666077},{"id":"https://openalex.org/keywords/convection-diffusion-equation","display_name":"advection-diffusion equation","score":0.9369999766349792},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"finite volume method","score":0.7850000262260437},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"finite difference method","score":0.6930000185966492},{"id":"https://openalex.org/keywords/grid-resolution-effects","display_name":"grid resolution effects","score":0.7839999794960022},{"id":"https://openalex.org/keywords/numerical-schemes","display_name":"numerical schemes","score":0.6359999775886536},{"id":"https://openalex.org/keywords/computational-fluid-dynamics","display_name":"computational fluid dynamics","score":0.8880000114440918}],"concepts":[{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.6836833357810974},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6586679220199585},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.6267901062965393},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5833616852760315},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5450234413146973},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5289478302001953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5274189710617065},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5249164700508118},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4728270471096039},{"id":"https://openalex.org/C154181440","wikidata":"https://www.wikidata.org/wiki/Q1683292","display_name":"Numerical differentiation","level":2,"score":0.4346785247325897},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4258239269256592},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3686986565589905},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28350508213043213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2432575821876526},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.13140922784805298},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10700491070747375},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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:10.1115/fedsm2013-16378","doi":"https://doi.org/10.1115/fedsm2013-16378","is_oa":false,"landing_page_url":"https://doi.org/10.1115/fedsm2013-16378","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Volume 1A, Symposia: Advances in Fluids Engineering Education; Advances in Numerical Modeling for Turbomachinery Flow Optimization; Applications in CFD; Bio-Inspired Fluid Mechanics; CFD Verification and Validation; Development and Applications of Immersed Boundary Methods; DNS, LES, and Hybrid RANS/LES Methods","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2008795316","https://openalex.org/W4381735293","https://openalex.org/W2075266379","https://openalex.org/W2404676059","https://openalex.org/W1968776920","https://openalex.org/W3096618578","https://openalex.org/W3044746972","https://openalex.org/W2504536853","https://openalex.org/W6945927620","https://openalex.org/W1012872135"],"abstract_inverted_index":{"Dual":[0],"number":[1,62,89,138,185],"arithmetic":[2],"is":[3,48,92,141,153,220,252,292],"a":[4,83,223,232,272,276],"well-known":[5],"strategy":[6],"for":[7,198,206],"automatic":[8,90,186,290],"differentiation":[9,91,291],"of":[10,21,29,36,53,69,95,98,117,129,133,158,166,172,212,269,282],"computer":[11,77,277],"codes":[12],"which":[13],"gives":[14],"exact":[15],"derivatives,":[16],"to":[17,27,49,56,82,110,178,231,241,258,262,271],"the":[18,22,30,51,57,67,70,76,80,96,99,103,107,112,118,130,144,163,173,190,207,237,243,246,267,286],"machine":[19],"accuracy,":[20],"computed":[23,217,288],"quantities":[24],"with":[25,176],"respect":[26,177],"any":[28],"involved":[31],"variables.":[32],"A":[33,147,279],"common":[34],"application":[35],"this":[37,213],"concept":[38],"in":[39,46,64,143,285],"Computational":[40],"Fluid":[41],"Dynamics,":[42],"or":[43],"numerical":[44,104,134,174,238,283],"modeling":[45],"general,":[47],"assess":[50],"sensitivity":[52,81,131,230,268],"mathematical":[54,72,101,224],"models":[55],"model":[58,84,119,225,233,273],"parameters.":[59],"However,":[60],"dual":[61,88,137,184],"arithmetic,":[63],"theory,":[65],"finds":[66],"derivatives":[68,191,211],"actual":[71,100],"expressions":[73],"evaluated":[74,181],"by":[75,87,124],"code.":[78,278],"Thus":[79],"parameter":[85,234,274],"found":[86,205],"essentially":[93],"that":[94,116,222],"combination":[97],"equations,":[102],"scheme":[105],"and":[106,162,210,245],"grid":[108,247],"used":[109],"solve":[111,242],"equations":[113,120,167,244],"not":[114],"just":[115],"alone":[121],"as":[122],"implied":[123],"some":[125],"studies.":[126],"This":[127,250],"aspect":[128],"analysis":[132],"simulations":[135],"using":[136,155,183,195,275,289],"auto":[139],"derivation":[140],"explored":[142],"current":[145],"study.":[146],"simple":[148],"one-dimensional":[149],"advection":[150],"diffusion":[151],"equation":[152],"discretized":[154],"different":[156,229],"schemes":[157],"finite":[159,196],"volume":[160],"method":[161,239],"resulting":[164],"systems":[165],"are":[168,180,192,215],"solved":[169],"numerically.":[170],"Derivatives":[171],"solutions":[175],"parameters":[179],"automatically":[182],"differentiation.":[187],"In":[188],"addition":[189],"also":[193,204,216],"estimated":[194],"differencing":[197],"comparison.":[199],"The":[200],"analytical":[201],"solution":[202,214],"was":[203],"original":[208],"PDE":[209],"analytically.":[218],"It":[219],"shown":[221],"could":[226],"potentially":[227],"show":[228],"depending":[235],"on":[236],"employed":[240],"resolution":[248],"used.":[249],"distinction":[251],"important":[253],"since":[254],"such":[255],"inter-dependence":[256],"needs":[257],"be":[259],"carefully":[260],"addressed":[261],"avoid":[263],"confusion":[264],"when":[265],"reporting":[266],"predictions":[270],"systematic":[280],"assessment":[281],"uncertainty":[284],"sensitivities":[287],"presented.":[293]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}