{"id":"https://openalex.org/W4410881362","doi":"https://doi.org/10.1515/cmam-2024-0198","title":"High-Order Accurate Structure-Preserving Finite Volume Scheme for Ten-Moment Gaussian Closure Equations with Source Terms: Positivity and Well-Balancedness","display_name":"High-Order Accurate Structure-Preserving Finite Volume Scheme for Ten-Moment Gaussian Closure Equations with Source Terms: Positivity and Well-Balancedness","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4410881362","doi":"https://doi.org/10.1515/cmam-2024-0198"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2024-0198","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0198","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5100361532","display_name":"Zhihao Zhang","orcid":"https://orcid.org/0000-0002-3038-3415"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihao Zhang","raw_affiliation_strings":["Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014339815","display_name":"Jiangfu Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiangfu Wang","raw_affiliation_strings":["Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109202774","display_name":"Huazhong Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huazhong Tang","raw_affiliation_strings":["Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Applied Physics and Technology, HEDPS and LMAM , School of Mathematical Sciences , 12465 Peking University , Beijing , 100871 , P. R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100361532"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":1.4093,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78535297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"25","issue":"3","first_page":"709","last_page":"740"},"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":0.9993000030517578,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9947999715805054,"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/closure","display_name":"Closure (psychology)","score":0.6829587817192078},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6707807779312134},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.6491028070449829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6064656972885132},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5378287434577942},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5124812126159668},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5060631632804871},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.44546476006507874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42284417152404785},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4200237989425659},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18906211853027344},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1250467598438263},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.1097995936870575},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09962797164916992},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.061263471841812134}],"concepts":[{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6829587817192078},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6707807779312134},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.6491028070449829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6064656972885132},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5378287434577942},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5124812126159668},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5060631632804871},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.44546476006507874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42284417152404785},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4200237989425659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18906211853027344},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1250467598438263},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1097995936870575},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09962797164916992},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.061263471841812134},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2024-0198","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2024-0198","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2519258023","display_name":null,"funder_award_id":"12288101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6137477588","display_name":null,"funder_award_id":"12171227","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6318382515","display_name":null,"funder_award_id":"2020YFA0712000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W232198546","https://openalex.org/W752645271","https://openalex.org/W1263959958","https://openalex.org/W1800640835","https://openalex.org/W1967073957","https://openalex.org/W1976632273","https://openalex.org/W1980103755","https://openalex.org/W1990790313","https://openalex.org/W1995214185","https://openalex.org/W1996468417","https://openalex.org/W2008956940","https://openalex.org/W2018823890","https://openalex.org/W2037019252","https://openalex.org/W2045979721","https://openalex.org/W2054362419","https://openalex.org/W2054597080","https://openalex.org/W2055380691","https://openalex.org/W2073378999","https://openalex.org/W2078033075","https://openalex.org/W2083367386","https://openalex.org/W2093706822","https://openalex.org/W2116729868","https://openalex.org/W2155785405","https://openalex.org/W2224008946","https://openalex.org/W2235936257","https://openalex.org/W2287490544","https://openalex.org/W2318625333","https://openalex.org/W2327700469","https://openalex.org/W2339363082","https://openalex.org/W2530578203","https://openalex.org/W2579422625","https://openalex.org/W2597037285","https://openalex.org/W2766378224","https://openalex.org/W2774377022","https://openalex.org/W2787270748","https://openalex.org/W2787833295","https://openalex.org/W2798758989","https://openalex.org/W2827482115","https://openalex.org/W2830553926","https://openalex.org/W2906968925","https://openalex.org/W2914187018","https://openalex.org/W2952800475","https://openalex.org/W2963031533","https://openalex.org/W3000033894","https://openalex.org/W3010934937","https://openalex.org/W3022343961","https://openalex.org/W3022479466","https://openalex.org/W3025882857","https://openalex.org/W3039108229","https://openalex.org/W3040091001","https://openalex.org/W3099299467","https://openalex.org/W3100529908","https://openalex.org/W3101661292","https://openalex.org/W3101707510","https://openalex.org/W3102733628","https://openalex.org/W3104660457","https://openalex.org/W3122532510","https://openalex.org/W3128823497","https://openalex.org/W3172003963","https://openalex.org/W3215639577","https://openalex.org/W4280627761","https://openalex.org/W4312996890","https://openalex.org/W4313255077","https://openalex.org/W4321481761","https://openalex.org/W4362549068","https://openalex.org/W4386034553","https://openalex.org/W4386101102","https://openalex.org/W4388453352","https://openalex.org/W4390821605","https://openalex.org/W4392245344","https://openalex.org/W4401074488","https://openalex.org/W4402738440","https://openalex.org/W4405302081","https://openalex.org/W4407217348"],"related_works":["https://openalex.org/W315394019","https://openalex.org/W2923398117","https://openalex.org/W4309585848","https://openalex.org/W2265383332","https://openalex.org/W4328130279","https://openalex.org/W2105009749","https://openalex.org/W4299387245","https://openalex.org/W2765469179","https://openalex.org/W583262921","https://openalex.org/W2036721792"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"develops":[3],"high-order":[4,233,262,288],"accurate":[5,49],"positivity-preserving":[6,50],"(PP)":[7],"and":[8,45,51,92,147,162,170,181,184,189,258,272,280,291],"well-balanced":[9,52],"(WB)":[10],"finite":[11],"volume":[12],"schemes":[13,55,74,100,135,191,234],"for":[14,56,121,132,168,192,254],"the":[15,25,29,33,36,79,95,103,110,118,133,144,148,155,210,225,232,240,248,251,255,261,265,287,297,301],"ten-moment":[16,57],"Gaussian":[17,58],"closure":[18,59],"equations":[19,60],"with":[20,61,84,89],"source":[21,62,96],"terms":[22],"based":[23,77,138],"on":[24,35,78,139,219],"prior":[26],"knowledge":[27],"of":[28,94,143,172,224,239,250,300],"equilibrium":[30,126],"states,":[31,87],"extending":[32],"work":[34],"discontinuous":[37,53],"Galerkin":[38,54],"method":[39],"in":[40,209,277],"[J.":[41],"Wang,":[42,278],"H.":[43,185],"Tang":[44,279],"K.":[46],"Wu,":[47],"High-order":[48],"terms,":[63],"J.":[64],"Comput.":[65],"Phys.":[66],"519":[67],"2024,":[68],"Article":[69],"ID":[70],"113451].":[71],"The":[72,98],"semi-discrete":[73],"are":[75],"constructed":[76],"Harten-Lax-van":[80],"Leer-Contact":[81],"(HLLC)":[82],"flux":[83,146],"modified":[85],"solution":[86],"along":[88],"suitable":[90],"discretization":[91],"decomposition":[93],"terms.":[97],"fully-discrete":[99,134],"obtained":[101],"by":[102],"explicit":[104],"strong-stability-preserving":[105],"Rung-Kutta":[106],"time":[107],"discretizations":[108],"(including":[109],"forward":[111],"Euler)":[112],"can":[113],"be":[114],"proved":[115],"to":[116,246,275],"maintain":[117],"WB":[119,290],"property":[120,253],"a":[122,236],"given":[123],"known":[124],"hydrostatic":[125],"state.":[127],"A":[128],"rigorous":[129],"PP":[130,252,267,292],"analysis":[131,169,268],"is":[136,269],"provided,":[137],"several":[140,220],"key":[141],"properties":[142,223,293],"HLLC":[145,226],"admissible":[149,211],"state":[150,212],"set":[151,213],"as":[152,154,294,296],"well":[153,295],"geometric":[156],"quasilinearlization":[157],"(GQL)":[158],"approach":[159],"[K.":[160,182],"Wu":[161,183,281],"C.-W.":[163],"Shu,":[164],"Geometric":[165],"quasilinearization":[166],"framework":[167],"design":[171],"bound-preserving":[173],"schemes,":[174],"SIAM":[175],"Rev.":[176],"65":[177],"2023,":[178],"4,":[179],"1031\u20131073]":[180],"Tang,":[186],"Admissible":[187],"states":[188],"physical-constraints-preserving":[190],"relativistic":[193],"magnetohydrodynamic":[194],"equations,":[195],"Math.":[196],"Models":[197],"Methods":[198],"Appl.":[199],"Sci.":[200],"27":[201],"2017,":[202],"10,":[203],"1871\u20131928]":[204],"transforming":[205],"complex":[206],"nonlinear":[207],"constraints":[208],"into":[214,235],"simple":[215,271],"linear":[216],"ones.":[217],"Based":[218],"newly":[221],"introduced":[222],"flux,":[227],"we":[228],"may":[229],"not":[230],"decompose":[231],"convex":[237],"combination":[238],"\u201cfirst-order":[241],"schemes\u201d,":[242],"which":[243],"permits":[244],"us":[245],"skip":[247],"proof":[249],"first-order":[256],"scheme":[257],"directly":[259],"analyze":[260],"schemes.":[263,303],"Consequently,":[264],"present":[266],"more":[270],"direct":[273],"compared":[274],"that":[276],"(2024).":[282],"Several":[283],"numerical":[284],"experiments":[285],"validate":[286],"accuracy,":[289],"high":[298],"resolution":[299],"proposed":[302]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}