{"id":"https://openalex.org/W2032650387","doi":"https://doi.org/10.1137/s1064827599357814","title":"A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves","display_name":"A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2032650387","doi":"https://doi.org/10.1137/s1064827599357814","mag":"2032650387"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599357814","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599357814","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/A5071853554","display_name":"Christiane Helzel","orcid":"https://orcid.org/0000-0002-9901-7149"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christiane Helzel","raw_affiliation_strings":["Otto von Guericke University Magdeburg\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke University Magdeburg\u00a0","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085592203","display_name":"Randall J. LeVeque","orcid":"https://orcid.org/0000-0003-1384-4504"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Randall J. Leveque","raw_affiliation_strings":["Otto von Guericke University Magdeburg\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto von Guericke University Magdeburg\u00a0","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048388377","display_name":"Gerald Warnecke","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gerald Warnecke","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4298,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.9687933,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"4","first_page":"1489","last_page":"1510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9988999962806702,"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":0.9988999962806702,"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":0.996999979019165,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/detonation","display_name":"Detonation","score":0.9397240877151489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6322468519210815},{"id":"https://openalex.org/keywords/godunovs-scheme","display_name":"Godunov's scheme","score":0.5900956392288208},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.5359362363815308},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.531821072101593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5135312676429749},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.4809338450431824},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.4749966859817505},{"id":"https://openalex.org/keywords/combustion","display_name":"Combustion","score":0.42348527908325195},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3977012634277344},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3901349902153015},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20531266927719116},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09677568078041077},{"id":"https://openalex.org/keywords/explosive-material","display_name":"Explosive material","score":0.08124354481697083}],"concepts":[{"id":"https://openalex.org/C203397868","wikidata":"https://www.wikidata.org/wiki/Q786054","display_name":"Detonation","level":3,"score":0.9397240877151489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6322468519210815},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.5900956392288208},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.5359362363815308},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.531821072101593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5135312676429749},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.4809338450431824},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.4749966859817505},{"id":"https://openalex.org/C105923489","wikidata":"https://www.wikidata.org/wiki/Q133235","display_name":"Combustion","level":2,"score":0.42348527908325195},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3977012634277344},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3901349902153015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20531266927719116},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09677568078041077},{"id":"https://openalex.org/C154238967","wikidata":"https://www.wikidata.org/wiki/Q12870","display_name":"Explosive material","level":2,"score":0.08124354481697083},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827599357814","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599357814","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":"Affordable and clean energy","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W87288849","https://openalex.org/W1510373280","https://openalex.org/W1529498073","https://openalex.org/W1532515344","https://openalex.org/W1554134448","https://openalex.org/W1584465342","https://openalex.org/W1595775464","https://openalex.org/W1973832069","https://openalex.org/W1994357965","https://openalex.org/W1996106164","https://openalex.org/W2013000460","https://openalex.org/W2025483160","https://openalex.org/W2026388260","https://openalex.org/W2033422827","https://openalex.org/W2034049222","https://openalex.org/W2034976587","https://openalex.org/W2038991247","https://openalex.org/W2044738523","https://openalex.org/W2056207357","https://openalex.org/W2062428473","https://openalex.org/W2067565344","https://openalex.org/W2077604686","https://openalex.org/W2080612171","https://openalex.org/W2083659289","https://openalex.org/W2094710134","https://openalex.org/W2148195085","https://openalex.org/W2156033209","https://openalex.org/W3036269677","https://openalex.org/W4231597745","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W4295135832","https://openalex.org/W2520772736","https://openalex.org/W4240076417","https://openalex.org/W2267387804","https://openalex.org/W2016488435","https://openalex.org/W2350290936","https://openalex.org/W4214690252","https://openalex.org/W1977614220","https://openalex.org/W3035499973","https://openalex.org/W2371649168"],"abstract_inverted_index":{"The":[0,94],"numerical":[1,9],"approximation":[2],"of":[3,18,26,50,78],"combustion":[4],"processes":[5],"may":[6],"lead":[7],"to":[8,84],"difficulties,":[10],"which":[11],"are":[12,73,110],"caused":[13],"by":[14,58],"different":[15],"time":[16,55,92],"scales":[17],"the":[19,23,27,48,59,65,76,79,99],"transport":[20],"part":[21,25],"and":[22,46,54,75,106],"reactive":[24],"model":[28],"equations.":[29],"Here":[30],"we":[31],"consider":[32],"a":[33,51,113,118],"modified":[34],"fractional":[35],"step":[36,56],"method":[37],"that":[38],"overcomes":[39],"this":[40],"difficulty":[41],"on":[42],"standard":[43],"test":[44],"problems":[45],"allows":[47],"use":[49],"mesh":[52],"width":[53],"determined":[57],"nonreactive":[60],"part,":[61],"without":[62],"precisely":[63],"resolving":[64],"very":[66],"small":[67],"reaction":[68],"zone.":[69],"High-resolution":[70],"Godunov":[71],"methods":[72],"employed":[74],"structure":[77],"Riemann":[80],"solution":[81],"is":[82,96],"used":[83],"determine":[85],"where":[86],"burning":[87],"should":[88],"occur":[89],"in":[90,98],"each":[91],"step.":[93],"modification":[95],"implemented":[97],"software":[100],"packageCLAWPACK.":[101],"Numerical":[102],"results":[103],"for":[104],"1D":[105],"2D":[107],"detonation":[108,114],"waves":[109],"shown,":[111],"including":[112],"wave":[115],"diffracting":[116],"around":[117],"corner.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":9}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}