{"id":"https://openalex.org/W1971166309","doi":"https://doi.org/10.1137/050628052","title":"Numerical methods for nonconservative hyperbolic systems: a theoretical framework.","display_name":"Numerical methods for nonconservative hyperbolic systems: a theoretical framework.","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1971166309","doi":"https://doi.org/10.1137/050628052","mag":"1971166309"},"language":"en","primary_location":{"id":"doi:10.1137/050628052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628052","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/A5011941405","display_name":"Carlos Par\u00e9s","orcid":"https://orcid.org/0000-0002-9545-5635"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carlos Par\u00e9s","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011941405"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.2663,"has_fulltext":false,"cited_by_count":513,"citation_normalized_percentile":{"value":0.99461156,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"44","issue":"1","first_page":"300","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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":0.9998000264167786,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9979000091552734,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9965999722480774,"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":0.8411391973495483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.761662483215332},{"id":"https://openalex.org/keywords/godunovs-scheme","display_name":"Godunov's scheme","score":0.6566586494445801},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5630070567131042},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5280143618583679},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5105708837509155},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.48393088579177856},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4575485587120056},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.44623667001724243},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4271078109741211},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3487493395805359},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23212414979934692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17457252740859985}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8411391973495483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.761662483215332},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.6566586494445801},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5630070567131042},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5280143618583679},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5105708837509155},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.48393088579177856},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4575485587120056},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.44623667001724243},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4271078109741211},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3487493395805359},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23212414979934692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17457252740859985},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050628052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628052","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W111720152","https://openalex.org/W115528814","https://openalex.org/W203446229","https://openalex.org/W348217116","https://openalex.org/W1555627060","https://openalex.org/W1580089077","https://openalex.org/W1963600029","https://openalex.org/W1968636195","https://openalex.org/W1975628738","https://openalex.org/W1981198157","https://openalex.org/W1983883036","https://openalex.org/W1988953714","https://openalex.org/W1989319725","https://openalex.org/W1994363333","https://openalex.org/W2018277869","https://openalex.org/W2021640059","https://openalex.org/W2024219079","https://openalex.org/W2030731178","https://openalex.org/W2031043673","https://openalex.org/W2041314330","https://openalex.org/W2043057066","https://openalex.org/W2047160746","https://openalex.org/W2048459778","https://openalex.org/W2049266244","https://openalex.org/W2051740894","https://openalex.org/W2060320511","https://openalex.org/W2066633407","https://openalex.org/W2068056613","https://openalex.org/W2070533863","https://openalex.org/W2073378999","https://openalex.org/W2077620382","https://openalex.org/W2081986598","https://openalex.org/W2084025336","https://openalex.org/W2112150873","https://openalex.org/W2118653974","https://openalex.org/W2136592480","https://openalex.org/W2152122438","https://openalex.org/W2155785405","https://openalex.org/W2482838170","https://openalex.org/W4245037559","https://openalex.org/W4250741917"],"related_works":["https://openalex.org/W632617093","https://openalex.org/W2364357611","https://openalex.org/W3144960475","https://openalex.org/W2111445914","https://openalex.org/W4231519251","https://openalex.org/W2043057066","https://openalex.org/W1986608005","https://openalex.org/W2029836409","https://openalex.org/W2020017862","https://openalex.org/W1569557351"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,23,32,52,63,69,79,82,87,96,105,109,124],"this":[3,40],"paper":[4],"is":[5,42,73,76,140],"to":[6,13,19,27,44],"provide":[7],"a":[8,77,125,131,137],"theoretical":[9],"framework":[10,41],"allowing":[11],"one":[12],"extend":[14],"some":[15,106],"general":[16,30,94,103,122],"concepts":[17],"related":[18],"the":[20,28,48,67,80,93,102,121],"numerical":[21,54,71],"approximation":[22],"1-d":[24],"conservation":[25,64,88],"laws":[26,59],"more":[29],"case":[31],"first":[33,132],"order":[34,127,133],"quasi-linear":[35],"hyperbolic":[36],"systems.":[37],"In":[38],"particular":[39],"intended":[43],"be":[45],"useful":[46],"for":[47,56,85],"design":[49],"and":[50,100,117,136],"analysis":[51],"well-balanced":[53],"schemes":[55,72,84,110],"solving":[57],"balance":[58],"or":[60],"coupled":[61],"systems":[62,86],"laws.":[65,89],"First,":[66],"concept":[68,81],"path-conservative":[70,134],"introduced,":[74],"which":[75],"generalization":[78],"conservative":[83],"Then,":[90],"we":[91],"introduce":[92],"definition":[95],"approximate":[97],"Riemann":[98],"solvers":[99],"give":[101],"expression":[104],"well-known":[107],"families":[108],"based":[111,129],"on":[112,130],"these":[113],"solvers:":[114],"Godunov,":[115],"Roe,":[116],"relaxation":[118],"methods.":[119],"Finally,":[120],"form":[123],"high":[126],"scheme":[128,135],"reconstruction":[138],"operator":[139],"presented.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":45},{"year":2024,"cited_by_count":43},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":31},{"year":2020,"cited_by_count":36},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":31},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":24},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":44},{"year":2012,"cited_by_count":24}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}