{"id":"https://openalex.org/W1983883036","doi":"https://doi.org/10.1137/040607642","title":"On Well\u2010Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems","display_name":"On Well\u2010Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1983883036","doi":"https://doi.org/10.1137/040607642","mag":"1983883036"},"language":"en","primary_location":{"id":"doi:10.1137/040607642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607642","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/A5005054247","display_name":"Manuel J. Castro","orcid":"https://orcid.org/0000-0003-3164-7715"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. J. Castro D\u00edaz","raw_affiliation_strings":["Dpto. An\u00e1lisis Matem\u00e1tico, Universidad de M\u00e1laga, Campus Teatinos s/n, M\u00e1laga, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. An\u00e1lisis Matem\u00e1tico, Universidad de M\u00e1laga, Campus Teatinos s/n, M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061387427","display_name":"Tom\u00e1s Chac\u00f3n Rebollo","orcid":"https://orcid.org/0000-0002-0784-1174"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"T. Chac\u00f3n Rebollo","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada I, Universidad de Sevilla. 41012 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada I, Universidad de Sevilla. 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080418633","display_name":"Enrique D. Fern\u00e1ndez-Nieto","orcid":"https://orcid.org/0000-0002-6944-4019"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. D. Fern\u00e1ndez\u2010Nieto","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada I, Universidad de Sevilla. 41012 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada I, Universidad de Sevilla. 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011941405","display_name":"Carlos Par\u00e9s","orcid":"https://orcid.org/0000-0002-9545-5635"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos Par\u00e9s","raw_affiliation_strings":["Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sevilla, Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2886,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.93456659,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"3","first_page":"1093","last_page":"1126"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9958000183105469,"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":0.9955000281333923,"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":0.8718427419662476},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5738750100135803},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5665959119796753},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.555743932723999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5218074321746826},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5113603472709656},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.5108222961425781},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.49175336956977844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4467158019542694},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4108119010925293},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.17197227478027344},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.0724630355834961}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8718427419662476},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5738750100135803},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5665959119796753},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.555743932723999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5218074321746826},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5113603472709656},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5108222961425781},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49175336956977844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4467158019542694},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4108119010925293},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.17197227478027344},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0724630355834961},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical 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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040607642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607642","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.571.946","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.571.946","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://anamat.cie.uma.es/publicaciones/2007_art02.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/6","score":0.550000011920929,"display_name":"Clean water and sanitation"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310967","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W111720152","https://openalex.org/W115528814","https://openalex.org/W1489409145","https://openalex.org/W1554134448","https://openalex.org/W1963600029","https://openalex.org/W2006837880","https://openalex.org/W2018277869","https://openalex.org/W2024219079","https://openalex.org/W2031043673","https://openalex.org/W2034976587","https://openalex.org/W2049266244","https://openalex.org/W2073378999","https://openalex.org/W2118617078","https://openalex.org/W2133429431","https://openalex.org/W2136592480","https://openalex.org/W2142452567","https://openalex.org/W2152122438","https://openalex.org/W2168496297"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W4255628145","https://openalex.org/W2382043075","https://openalex.org/W2809151339","https://openalex.org/W2216913934","https://openalex.org/W2360673138","https://openalex.org/W2809370583","https://openalex.org/W4301447905"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"introduce":[4],"a":[5,40],"general":[6],"family":[7],"of":[8,23],"finite":[9],"volume":[10],"methods":[11],"for":[12,39,72],"nonhomogeneous":[13],"hyperbolic":[14],"systems":[15],"with":[16,63,81],"nonconservative":[17],"terms.":[18],"We":[19],"prove":[20],"that":[21],"all":[22,30,35],"them":[24],"are":[25,70],"\u201casymptotically":[26],"well\u2010balanced\u201d:":[27],"they":[28],"preserve":[29],"smooth":[31],"stationary":[32],"solutions":[33],"in":[34],"the":[36,59,78],"domain":[37],"except":[38],"set":[41],"whose":[42],"measure":[43],"tends":[44,50],"to":[45,51,57],"zero":[46],"as":[47],"$\\Delta":[48],"x$":[49],"zero.":[52],"This":[53],"theory":[54],"is":[55],"applied":[56],"solve":[58],"bilayer":[60],"shallow\u2010water":[61],"equations":[62],"arbitrary":[64],"cross\u2010section.":[65],"Finally,":[66],"some":[67],"numerical":[68],"tests":[69],"presented":[71],"simplified":[73],"but":[74],"meaningful":[75],"geometries,":[76],"comparing":[77],"computed":[79],"solution":[80],"approximated":[82],"asymptotic":[83],"analytical":[84],"solutions.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}