{"id":"https://openalex.org/W2012483346","doi":"https://doi.org/10.1137/050648201","title":"Lie Symmetry Preservation and Shock-Capturing Methods","display_name":"Lie Symmetry Preservation and Shock-Capturing Methods","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2012483346","doi":"https://doi.org/10.1137/050648201","mag":"2012483346"},"language":"en","primary_location":{"id":"doi:10.1137/050648201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050648201","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/A5101820517","display_name":"Ran Zheng","orcid":"https://orcid.org/0000-0001-7786-5094"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zheng Ran","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101820517"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.91,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85315486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"1","first_page":"325","last_page":"343"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.996399998664856,"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/inviscid-flow","display_name":"Inviscid flow","score":0.917361319065094},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.793114423751831},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.6620291471481323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.656394362449646},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6095967888832092},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.5247029066085815},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.49680569767951965},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.4750150144100189},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42739251255989075},{"id":"https://openalex.org/keywords/symmetry-breaking","display_name":"Symmetry breaking","score":0.41979870200157166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3438730239868164},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34088194370269775},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2567012906074524},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24185189604759216},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19371795654296875},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14094069600105286},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07509967684745789}],"concepts":[{"id":"https://openalex.org/C86252789","wikidata":"https://www.wikidata.org/wiki/Q2247765","display_name":"Inviscid flow","level":2,"score":0.917361319065094},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.793114423751831},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.6620291471481323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.656394362449646},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6095967888832092},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5247029066085815},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.49680569767951965},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.4750150144100189},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42739251255989075},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.41979870200157166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3438730239868164},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34088194370269775},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2567012906074524},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24185189604759216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19371795654296875},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14094069600105286},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07509967684745789},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050648201","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050648201","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"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300015738/16","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300015738/16&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W44173220","https://openalex.org/W228777157","https://openalex.org/W614805704","https://openalex.org/W1495727713","https://openalex.org/W1639469298","https://openalex.org/W1678181739","https://openalex.org/W1685328395","https://openalex.org/W1971200802","https://openalex.org/W1973481688","https://openalex.org/W1975106615","https://openalex.org/W1978841144","https://openalex.org/W1990945307","https://openalex.org/W1991248531","https://openalex.org/W1993602386","https://openalex.org/W1998830482","https://openalex.org/W1999399767","https://openalex.org/W2001138128","https://openalex.org/W2005106153","https://openalex.org/W2007172865","https://openalex.org/W2017912972","https://openalex.org/W2020168202","https://openalex.org/W2031171101","https://openalex.org/W2053018511","https://openalex.org/W2054662916","https://openalex.org/W2066483416","https://openalex.org/W2070605055","https://openalex.org/W2439399157","https://openalex.org/W2749486094","https://openalex.org/W2949694649","https://openalex.org/W3010292040","https://openalex.org/W3100632400","https://openalex.org/W3104396999","https://openalex.org/W3123589552"],"related_works":["https://openalex.org/W1486213812","https://openalex.org/W2963995572","https://openalex.org/W2804509140","https://openalex.org/W3011178584","https://openalex.org/W2118166611","https://openalex.org/W1979767191","https://openalex.org/W2030648747","https://openalex.org/W3011550360","https://openalex.org/W3166508280","https://openalex.org/W3119573441"],"abstract_inverted_index":{"It":[0],"is":[1,34,89],"known":[2],"that":[3,18],"some":[4],"traditional":[5],"shock-capturing":[6],"schemes,":[7,12],"including":[8],"Godunov-":[9],"or":[10],"Roe-type":[11],"generate":[13],"downstream":[14],"oscillatory":[15],"wave":[16],"patterns":[17,44],"cannot":[19],"be":[20],"effectively":[21],"dampened":[22],"by":[23],"the":[24,37,46,50,54,69,78,95,99,103,106],"dissipation":[25],"methods":[26],"they":[27],"provide.":[28],"The":[29],"theme":[30],"of":[31,49,98,105],"this":[32],"paper":[33,57],"to":[35],"understand":[36],"formation":[38],"and":[39,61,72,81],"behavior":[40],"at":[41],"these":[42],"upstream/downstream":[43],"from":[45],"point":[47],"view":[48],"symmetry":[51,59],"inherent":[52,96],"in":[53,64,102],"PDE.":[55],"This":[56],"investigates":[58],"breaking":[60,88],"spatial":[62],"oscillations":[63,101],"finite":[65],"difference":[66],"solutions":[67],"for":[68,94],"inviscid":[70],"Burgers":[71],"one-dimensional":[73],"Navier\u2013Stokes":[74],"shock":[75],"equations":[76],"using":[77],"Lax\u2013Wendroff,":[79],"TVD,":[80],"nonoscillatory,":[82],"nonfree":[83],"parameter":[84],"dissipative":[85],"schemes.":[86],"Symmetry":[87],"considered":[90],"as":[91],"a":[92],"candidate":[93],"cause":[97],"nonphysical":[100],"vicinity":[104],"shock.":[107]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}