{"id":"https://openalex.org/W1479766746","doi":"https://doi.org/10.1090/mcom/2970","title":"Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws","display_name":"Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws","publication_year":2015,"publication_date":"2015-05-13","ids":{"openalex":"https://openalex.org/W1479766746","doi":"https://doi.org/10.1090/mcom/2970","mag":"1479766746"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/2970","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2970","pdf_url":"https://www.ams.org/mcom/2016-85-297/S0025-5718-2015-02970-6/S0025-5718-2015-02970-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2016-85-297/S0025-5718-2015-02970-6/S0025-5718-2015-02970-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038195170","display_name":"Claus R. Goetz","orcid":null},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Claus Goetz","raw_affiliation_strings":["Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, I-38123 Trento, Italy","Department of Civil, Environmental and Mechanical Engineering University of Trento Via Mesiano, 77 I\u201038123 Trento Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, I-38123 Trento, Italy","institution_ids":["https://openalex.org/I193223587"]},{"raw_affiliation_string":"Department of Civil, Environmental and Mechanical Engineering University of Trento Via Mesiano, 77 I\u201038123 Trento Italy","institution_ids":["https://openalex.org/I193223587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028418165","display_name":"Armin Iske","orcid":"https://orcid.org/0000-0003-1743-5484"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Armin Iske","raw_affiliation_strings":["Department of Mathematics, University of Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany","Dept. of Mathematics, University of Hamburg, Bundesstr. 55, D\u201320146 Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Dept. of Mathematics, University of Hamburg, Bundesstr. 55, D\u201320146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5554,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91658047,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"85","issue":"297","first_page":"35","last_page":"62"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9990000128746033,"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":0.9990000128746033,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9975000023841858,"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":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.8322916626930237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7811440229415894},{"id":"https://openalex.org/keywords/riemann-solver","display_name":"Riemann solver","score":0.77934330701828},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.698444128036499},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6976336240768433},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.6289960145950317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6257323026657104},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5711374282836914},{"id":"https://openalex.org/keywords/roe-solver","display_name":"Roe solver","score":0.4958404004573822},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.48965078592300415},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4662211239337921},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3930794298648834},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.2894156575202942},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18203401565551758},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17478424310684204},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07471197843551636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07342806458473206}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8322916626930237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7811440229415894},{"id":"https://openalex.org/C120796332","wikidata":"https://www.wikidata.org/wiki/Q6153788","display_name":"Riemann solver","level":3,"score":0.77934330701828},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.698444128036499},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6976336240768433},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.6289960145950317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6257323026657104},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5711374282836914},{"id":"https://openalex.org/C171520575","wikidata":"https://www.wikidata.org/wiki/Q7357538","display_name":"Roe solver","level":4,"score":0.4958404004573822},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.48965078592300415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4662211239337921},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3930794298648834},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.2894156575202942},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18203401565551758},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17478424310684204},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07471197843551636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07342806458473206},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/2970","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2970","pdf_url":"https://www.ams.org/mcom/2016-85-297/S0025-5718-2015-02970-6/S0025-5718-2015-02970-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.6494","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.6494","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-hamburg.de/home/iske/papers/approxGRP.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.406.99","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.99","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-hamburg.de/home/iske/papers/approx_grp.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/mcom/2970","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/2970","pdf_url":"https://www.ams.org/mcom/2016-85-297/S0025-5718-2015-02970-6/S0025-5718-2015-02970-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1479766746.pdf","grobid_xml":"https://content.openalex.org/works/W1479766746.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W191599861","https://openalex.org/W1490657362","https://openalex.org/W1513760541","https://openalex.org/W1537224157","https://openalex.org/W1575881461","https://openalex.org/W1584487167","https://openalex.org/W1600967930","https://openalex.org/W1601617262","https://openalex.org/W1759894779","https://openalex.org/W1971334156","https://openalex.org/W1975576055","https://openalex.org/W1997030420","https://openalex.org/W1999399767","https://openalex.org/W2010334247","https://openalex.org/W2011669849","https://openalex.org/W2029465969","https://openalex.org/W2037470843","https://openalex.org/W2038291664","https://openalex.org/W2038501569","https://openalex.org/W2038991247","https://openalex.org/W2039150507","https://openalex.org/W2041669594","https://openalex.org/W2045849310","https://openalex.org/W2047691393","https://openalex.org/W2048941652","https://openalex.org/W2052013840","https://openalex.org/W2054662916","https://openalex.org/W2057412099","https://openalex.org/W2059398012","https://openalex.org/W2066051257","https://openalex.org/W2068255553","https://openalex.org/W2073945818","https://openalex.org/W2083435844","https://openalex.org/W2094184168","https://openalex.org/W2112548197","https://openalex.org/W2116530141","https://openalex.org/W2163199591","https://openalex.org/W2280082143","https://openalex.org/W2481459718","https://openalex.org/W2492550098","https://openalex.org/W3021722416","https://openalex.org/W4210744120","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W569491316","https://openalex.org/W4295135832","https://openalex.org/W1980365163","https://openalex.org/W2357877681","https://openalex.org/W3209871457","https://openalex.org/W2036623811","https://openalex.org/W2074800504","https://openalex.org/W2133986346","https://openalex.org/W2379245068","https://openalex.org/W4385807557"],"abstract_inverted_index":{"We":[0,43,103],"study":[1],"analytical":[2],"properties":[3],"of":[4,17,61,80,96],"the":[5,15,18,30,52,56,68,78,81,84,94,100,109],"Toro-Titarev":[6,31,53,69,101],"solver":[7,32,54,70],"for":[8,46,65,112,144],"generalized":[9,23],"Riemann":[10],"problems":[11,49],"(GRPs),":[12],"which":[13],"is":[14],"heart":[16],"flux":[19],"computation":[20],"in":[21,50,83,99],"ADER":[22],"Godunov":[24],"schemes.":[25],"In":[26],"particular,":[27],"we":[28],"compare":[29],"with":[33],"a":[34,113,149],"local":[35],"asymptotic":[36],"expansion":[37,60],"developed":[38],"by":[39,107],"LeFloch":[40],"and":[41,141,148],"Raviart.":[42],"show":[44],"that":[45],"nonlinear":[47,66,114],"scalar":[48],"1D":[51],"reproduces":[55],"truncated":[57],"Taylor":[58],"series":[59],"LeFloch-Raviart":[62],"exactly,":[63],"whereas":[64],"systems":[67],"introduces":[71],"an":[72],"error":[73],"whose":[74],"size":[75],"depends":[76],"on":[77],"height":[79],"jump":[82],"initial":[85],"data.":[86],"Thereby,":[87],"our":[88,105],"analysis":[89,111],"answers":[90],"open":[91],"questions":[92],"concerning":[93],"justification":[95],"simplifying":[97],"steps":[98],"solver.":[102],"illustrate":[104],"results":[106,143],"giving":[108],"full":[110],"<inline-formula":[115,128],"content-type=\"math/mathml\">":[116,129],"<mml:math":[117,130],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[118,131],"alttext=\"2\">":[119,132],"<mml:semantics>":[120,133],"<mml:mn>2</mml:mn>":[121,134],"<mml:annotation":[122,135],"encoding=\"application/x-tex\">2</mml:annotation>":[123,136],"</mml:semantics>":[124,137],"</mml:math>":[125,138],"</inline-formula>":[126,139],"-by-":[127],"system":[140,150],"numerical":[142],"shallow":[145],"water":[146],"equations":[147],"from":[151],"traffic":[152],"flow.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}