{"id":"https://openalex.org/W1985652000","doi":"https://doi.org/10.1137/s1064827502416113","title":"Discontinuous Galerkin BGK Method for Viscous Flow Equations: One-Dimensional Systems","display_name":"Discontinuous Galerkin BGK Method for Viscous Flow Equations: One-Dimensional Systems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1985652000","doi":"https://doi.org/10.1137/s1064827502416113","mag":"1985652000"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502416113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502416113","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/A5038382239","display_name":"Kun Xu","orcid":"https://orcid.org/0000-0002-3985-739X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kun Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038382239"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7522,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.81995662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"6","first_page":"1941","last_page":"1963"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":1.0,"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":1.0,"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":0.9991999864578247,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9986000061035156,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8940658569335938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7510923147201538},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6485745906829834},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5909281373023987},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5646986961364746},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5153250098228455},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5007500648498535},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4703139364719391},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46455973386764526},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.44877350330352783},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4480656385421753},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.38426750898361206},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.37440261244773865},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19585692882537842},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.18692156672477722},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18285906314849854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16375550627708435}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8940658569335938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7510923147201538},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6485745906829834},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5909281373023987},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5646986961364746},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5153250098228455},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5007500648498535},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4703139364719391},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46455973386764526},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.44877350330352783},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4480656385421753},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.38426750898361206},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.37440261244773865},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19585692882537842},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.18692156672477722},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18285906314849854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16375550627708435},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827502416113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502416113","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:repository.hkust.edu.hk:1783.1-21662","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-21662","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W4115567","https://openalex.org/W48075625","https://openalex.org/W1676298003","https://openalex.org/W1963857134","https://openalex.org/W1973481688","https://openalex.org/W1982465309","https://openalex.org/W2010107363","https://openalex.org/W2010726731","https://openalex.org/W2011125167","https://openalex.org/W2012938047","https://openalex.org/W2017700359","https://openalex.org/W2041822426","https://openalex.org/W2058487438","https://openalex.org/W2060608572","https://openalex.org/W2066060292","https://openalex.org/W2070854540","https://openalex.org/W2079263908","https://openalex.org/W2083659289","https://openalex.org/W2089134771","https://openalex.org/W2158574387","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2371200319","https://openalex.org/W2367609594","https://openalex.org/W2350320737","https://openalex.org/W3140967440","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2292863065","https://openalex.org/W2888482338","https://openalex.org/W2334254610"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"about":[3],"the":[4,13,20,23,33,41,45,52,56,62,67,76,84,87,91,99],"construction":[5],"of":[6,50,78],"a":[7],"BGK":[8],"Navier--Stokes":[9,102],"(BGK-NS)":[10],"solver":[11],"in":[12,19,36,44,55,70,83],"discontinuous":[14,58],"Galerkin":[15,59],"(DG)":[16],"framework.":[17],"Since":[18],"DG":[21],"formulation":[22],"conservative":[24],"variables":[25,43],"and":[26,80],"their":[27],"slopes":[28],"can":[29],"be":[30,105],"updated":[31],"simultaneously,":[32],"flow":[34,42],"evolution":[35],"each":[37],"element":[38],"involves":[39],"only":[40],"nearest":[46],"neighboring":[47],"cells.":[48],"Instead":[49],"using":[51],"semidiscrete":[53],"approach":[54],"Runge--Kutta":[57],"(RKDG)":[60],"method,":[61],"current":[63],"DG-BGK":[64,88],"method":[65,89],"integrates":[66],"governing":[68,93],"equations":[69,94],"time":[71],"as":[72],"well.":[73],"Due":[74],"to":[75],"coupling":[77],"advection":[79],"dissipative":[81],"terms":[82],"gas-kinetic":[85],"formulation,":[86],"solves":[90],"viscous":[92],"directly.":[95],"Numerical":[96],"examples":[97],"for":[98],"one-dimensional":[100],"compressible":[101],"solutions":[103],"will":[104],"presented.":[106]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}