{"id":"https://openalex.org/W4313421237","doi":"https://doi.org/10.1007/s42967-022-00210-4","title":"Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems","display_name":"Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems","publication_year":2022,"publication_date":"2022-12-28","ids":{"openalex":"https://openalex.org/W4313421237","doi":"https://doi.org/10.1007/s42967-022-00210-4"},"language":"en","primary_location":{"id":"doi:10.1007/s42967-022-00210-4","doi":"https://doi.org/10.1007/s42967-022-00210-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s42967-022-00210-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210175860","display_name":"Communications on Applied Mathematics and Computation","issn_l":"2096-6385","issn":["2096-6385","2661-8893"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-20","russia-white-list-3","vabb-shw"],"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":"Communications on Applied Mathematics and Computation","raw_type":"journal-article"},"volume":null,"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/A5018452636","display_name":"Gui\u2010Qiang Chen","orcid":"https://orcid.org/0000-0001-5146-3839","observed_orcids":["https://orcid.org/0000-0001-5146-3839"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Gui-Qiang G. Chen","raw_affiliation_strings":["Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, Oxford, UK","Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK"],"raw_orcid":"https://orcid.org/0000-0001-5146-3839","affiliations":[{"raw_affiliation_string":"Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Oxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018452636"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":null,"fwci":0.1342,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.32709822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"5","issue":"3","first_page":"1015","last_page":"1052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.8871999979019165,"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":0.8871999979019165,"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":0.05510000139474869,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.011099999770522118,"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/two-dimensional-riemann-problem","display_name":"two-dimensional Riemann problem","score":0.9049999713897705},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"free boundary problem","score":0.9789999723434448},{"id":"https://openalex.org/keywords/nonlinear-hyperbolic-conservation-laws","display_name":"nonlinear hyperbolic conservation laws","score":0.8399999737739563},{"id":"https://openalex.org/keywords/global-solutions","display_name":"global solutions","score":0.9259999990463257},{"id":"https://openalex.org/keywords/mixed-elliptic-hyperbolic-equations","display_name":"mixed elliptic-hyperbolic equations","score":0.9150000214576721},{"id":"https://openalex.org/keywords/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.7990000247955322}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8647503852844238},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.8525302410125732},{"id":"https://openalex.org/C103838597","wikidata":"https://www.wikidata.org/wiki/Q1579556","display_name":"Transonic","level":3,"score":0.7977200746536255},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6302585601806641},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6101281642913818},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.6099414825439453},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5903590321540833},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.5757815837860107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5692365765571594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5589957237243652},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.5564108490943909},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49232590198516846},{"id":"https://openalex.org/C112468886","wikidata":"https://www.wikidata.org/wiki/Q5535485","display_name":"Geometric function theory","level":3,"score":0.48208051919937134},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4607125222682953},{"id":"https://openalex.org/C120796332","wikidata":"https://www.wikidata.org/wiki/Q6153788","display_name":"Riemann solver","level":3,"score":0.442188560962677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28282928466796875},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12712815403938293},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.059580475091934204},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s42967-022-00210-4","doi":"https://doi.org/10.1007/s42967-022-00210-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s42967-022-00210-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210175860","display_name":"Communications on Applied Mathematics and Computation","issn_l":"2096-6385","issn":["2096-6385","2661-8893"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-20","russia-white-list-3","vabb-shw"],"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":"Communications on Applied Mathematics and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Life on land","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/15"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G100856787","display_name":"DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications","funder_award_id":"EP/V051121/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1327798365","display_name":"EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications","funder_award_id":"EP/L015811/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1838992689","display_name":null,"funder_award_id":"EP/V008854/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6860964818","display_name":null,"funder_award_id":"EP/V051121/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7343709596","display_name":"Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations","funder_award_id":"EP/V008854/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W205360716","https://openalex.org/W305332711","https://openalex.org/W655600474","https://openalex.org/W1250026354","https://openalex.org/W1482558098","https://openalex.org/W1501711999","https://openalex.org/W1532935311","https://openalex.org/W1561374308","https://openalex.org/W1591390169","https://openalex.org/W1591554063","https://openalex.org/W1601100443","https://openalex.org/W1647409653","https://openalex.org/W1970322878","https://openalex.org/W1970440866","https://openalex.org/W1970695124","https://openalex.org/W1974909005","https://openalex.org/W1982227924","https://openalex.org/W1983430582","https://openalex.org/W1984952381","https://openalex.org/W1985600324","https://openalex.org/W1989213383","https://openalex.org/W1990142375","https://openalex.org/W1990739729","https://openalex.org/W1999399767","https://openalex.org/W2003926361","https://openalex.org/W2015423868","https://openalex.org/W2019482884","https://openalex.org/W2022504593","https://openalex.org/W2026636263","https://openalex.org/W2027379249","https://openalex.org/W2027589535","https://openalex.org/W2027750003","https://openalex.org/W2030403041","https://openalex.org/W2033211444","https://openalex.org/W2034976587","https://openalex.org/W2040412963","https://openalex.org/W2041423792","https://openalex.org/W2042601893","https://openalex.org/W2058574380","https://openalex.org/W2059060905","https://openalex.org/W2062154247","https://openalex.org/W2065449706","https://openalex.org/W2066741072","https://openalex.org/W2066784287","https://openalex.org/W2075776956","https://openalex.org/W2080230957","https://openalex.org/W2087087179","https://openalex.org/W2094432683","https://openalex.org/W2104913690","https://openalex.org/W2106961716","https://openalex.org/W2128399324","https://openalex.org/W2145821666","https://openalex.org/W2157862867","https://openalex.org/W2169157063","https://openalex.org/W2189691319","https://openalex.org/W2331617037","https://openalex.org/W2596576480","https://openalex.org/W2783746118","https://openalex.org/W2963749583","https://openalex.org/W2998552826","https://openalex.org/W3012021409","https://openalex.org/W3022276623","https://openalex.org/W3035614913","https://openalex.org/W3047085143","https://openalex.org/W3083359600","https://openalex.org/W3093868708","https://openalex.org/W3101662633","https://openalex.org/W3110038039","https://openalex.org/W3127675355","https://openalex.org/W3163195093","https://openalex.org/W3167033636","https://openalex.org/W3200255304","https://openalex.org/W4238313514","https://openalex.org/W4292081050","https://openalex.org/W4292360407","https://openalex.org/W6600292188","https://openalex.org/W6942197816"],"related_works":["https://openalex.org/W3195766120","https://openalex.org/W569491316","https://openalex.org/W2036623811","https://openalex.org/W1980365163","https://openalex.org/W4295135832","https://openalex.org/W3027764204","https://openalex.org/W2357877681","https://openalex.org/W4386790333","https://openalex.org/W1967345874","https://openalex.org/W3013871708"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}