{"id":"https://openalex.org/W2106787187","doi":"https://doi.org/10.1007/s00211-007-0108-8","title":"A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework","display_name":"A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework","publication_year":2007,"publication_date":"2007-09-25","ids":{"openalex":"https://openalex.org/W2106787187","doi":"https://doi.org/10.1007/s00211-007-0108-8","mag":"2106787187"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-007-0108-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0108-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5005991575","display_name":"Fran\u00e7ois Bouchut","orcid":"https://orcid.org/0000-0002-2545-1655"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Bouchut","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques et Applications, CNRS and Ecole Normale Sup\u00e9rieure, 45 rue d\u2019Ulm, 75230, Paris Cedex 05, France","CNRS and Ecole Normale Sup\u00e9rieure, D\u00e9partement de Math\u00e9matiques et Applications, 45 rue d\u2019Ulm, 75230, Paris Cedex 05, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et Applications, CNRS and Ecole Normale Sup\u00e9rieure, 45 rue d\u2019Ulm, 75230, Paris Cedex 05, France","institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS and Ecole Normale Sup\u00e9rieure, D\u00e9partement de Math\u00e9matiques et Applications, 45 rue d\u2019Ulm, 75230, Paris Cedex 05, France#TAB#","institution_ids":["https://openalex.org/I29607241","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089167718","display_name":"Christian Klingenberg","orcid":"https://orcid.org/0000-0003-2033-8204"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Klingenberg","raw_affiliation_strings":["Departement of Mathematics, W\u00fcrzburg University, Am Hubland, 97074, W\u00fcrzburg, Germany","W\u00fcrzburg University, Departement of Mathematics, Am Hubland, 97074, W\u00fcrzburg, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departement of Mathematics, W\u00fcrzburg University, Am Hubland, 97074, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"W\u00fcrzburg University, Departement of Mathematics, Am Hubland, 97074, W\u00fcrzburg, Germany#TAB#","institution_ids":["https://openalex.org/I25974101"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089424158","display_name":"Knut Waagan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Knut Waagan","raw_affiliation_strings":["Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316, Oslo, Norway","Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316, Oslo, Norway#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316, Oslo, Norway","institution_ids":[]},{"raw_affiliation_string":"Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316, Oslo, Norway#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089424158"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.0052,"has_fulltext":false,"cited_by_count":133,"citation_normalized_percentile":{"value":0.96406924,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"108","issue":"1","first_page":"7","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9995999932289124,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9951000213623047,"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/riemann-solver","display_name":"Riemann solver","score":0.860598087310791},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.7962096929550171},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.7020170092582703},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.6672238707542419},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6576558351516724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6409161686897278},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.6251348853111267},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5668314695358276},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5180454254150391},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5156053900718689},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49101924896240234},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4734056890010834},{"id":"https://openalex.org/keywords/roe-solver","display_name":"Roe solver","score":0.4380875825881958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3702585697174072},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2591734528541565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16397017240524292},{"id":"https://openalex.org/keywords/plasma","display_name":"Plasma","score":0.13792657852172852},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.11783236265182495},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.09398430585861206},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0763126015663147}],"concepts":[{"id":"https://openalex.org/C120796332","wikidata":"https://www.wikidata.org/wiki/Q6153788","display_name":"Riemann solver","level":3,"score":0.860598087310791},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.7962096929550171},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.7020170092582703},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.6672238707542419},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6576558351516724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6409161686897278},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6251348853111267},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5668314695358276},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5180454254150391},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5156053900718689},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49101924896240234},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4734056890010834},{"id":"https://openalex.org/C171520575","wikidata":"https://www.wikidata.org/wiki/Q7357538","display_name":"Roe solver","level":4,"score":0.4380875825881958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3702585697174072},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2591734528541565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16397017240524292},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.13792657852172852},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.11783236265182495},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.09398430585861206},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0763126015663147},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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":2,"locations":[{"id":"doi:10.1007/s00211-007-0108-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0108-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.230.800","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.230.800","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ntnu.no/conservation/2006/043.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W104652564","https://openalex.org/W348217116","https://openalex.org/W1537224157","https://openalex.org/W1583892864","https://openalex.org/W1969760987","https://openalex.org/W1970142243","https://openalex.org/W1982236257","https://openalex.org/W1986742199","https://openalex.org/W1997690237","https://openalex.org/W2010714961","https://openalex.org/W2013770958","https://openalex.org/W2016922024","https://openalex.org/W2031208469","https://openalex.org/W2039471641","https://openalex.org/W2043057066","https://openalex.org/W2049803546","https://openalex.org/W2054988599","https://openalex.org/W2056665075","https://openalex.org/W2059036784","https://openalex.org/W2059049415","https://openalex.org/W2065075601","https://openalex.org/W2067207246","https://openalex.org/W2073447845","https://openalex.org/W2083898342","https://openalex.org/W2088432916","https://openalex.org/W2171431553","https://openalex.org/W2482838170","https://openalex.org/W2989887575"],"related_works":["https://openalex.org/W2085037704","https://openalex.org/W1663225052","https://openalex.org/W3164279712","https://openalex.org/W2010276774","https://openalex.org/W2067345573","https://openalex.org/W2133986346","https://openalex.org/W1990653832","https://openalex.org/W2022095181","https://openalex.org/W2379245068","https://openalex.org/W947788391"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}