{"id":"https://openalex.org/W3131264590","doi":"https://doi.org/10.1137/21m1398495","title":"Numerical Solver for the Boltzmann Equation with Self-Adaptive Collision Operators","display_name":"Numerical Solver for the Boltzmann Equation with Self-Adaptive Collision Operators","publication_year":2022,"publication_date":"2022-03-17","ids":{"openalex":"https://openalex.org/W3131264590","doi":"https://doi.org/10.1137/21m1398495","mag":"3131264590"},"language":"en","primary_location":{"id":"doi:10.1137/21m1398495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1398495","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/A5025938442","display_name":"Zhenning Cai","orcid":"https://orcid.org/0000-0002-7086-7983"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhenning Cai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100413387","display_name":"Yanli Wang","orcid":"https://orcid.org/0000-0003-2211-0254"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yanli Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025938442"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3515,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.41759794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"44","issue":"2","first_page":"B275","last_page":"B309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":1.0,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9943000078201294,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9872999787330627,"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/collision","display_name":"Collision","score":0.8025830984115601},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.667524516582489},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.6579744219779968},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5681137442588806},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5672414302825928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49641019105911255},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4907902181148529},{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.45910975337028503},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4291062355041504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.386520117521286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.299805611371994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19681504368782043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12187054753303528},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11218127608299255},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07847359776496887}],"concepts":[{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.8025830984115601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.667524516582489},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.6579744219779968},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5681137442588806},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5672414302825928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49641019105911255},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4907902181148529},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.45910975337028503},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4291062355041504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.386520117521286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.299805611371994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19681504368782043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12187054753303528},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11218127608299255},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07847359776496887},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1398495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1398495","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1258155048","display_name":null,"funder_award_id":"TZ2016002","funder_id":"https://openalex.org/F4320336025","funder_display_name":"Science Challenge Project"},{"id":"https://openalex.org/G2348786252","display_name":null,"funder_award_id":"12171026","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4797210442","display_name":null,"funder_award_id":"U1930402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G760993436","display_name":null,"funder_award_id":"R-146-000-326-112","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G7627071985","display_name":null,"funder_award_id":"12031013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7633250875","display_name":null,"funder_award_id":"R-146-000-305-114","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336025","display_name":"Science Challenge Project","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1555627060","https://openalex.org/W1584813075","https://openalex.org/W1965550492","https://openalex.org/W2015903283","https://openalex.org/W2019223612","https://openalex.org/W2026554882","https://openalex.org/W2032827682","https://openalex.org/W2036898921","https://openalex.org/W2038196379","https://openalex.org/W2039308004","https://openalex.org/W2043057066","https://openalex.org/W2043953726","https://openalex.org/W2058023939","https://openalex.org/W2058463720","https://openalex.org/W2083597099","https://openalex.org/W2085955212","https://openalex.org/W2085996766","https://openalex.org/W2092349685","https://openalex.org/W2131947874","https://openalex.org/W2134306372","https://openalex.org/W2159746144","https://openalex.org/W2171215286","https://openalex.org/W2313638164","https://openalex.org/W2609538046","https://openalex.org/W2735613905","https://openalex.org/W2766701282","https://openalex.org/W2789802199","https://openalex.org/W2794578566","https://openalex.org/W2893649682","https://openalex.org/W2963068646","https://openalex.org/W2963446664","https://openalex.org/W2963761797","https://openalex.org/W2970663352","https://openalex.org/W2998973082","https://openalex.org/W3003939291","https://openalex.org/W3021082965","https://openalex.org/W3089714836","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2186864281","https://openalex.org/W650625605","https://openalex.org/W3113932901","https://openalex.org/W4255427455","https://openalex.org/W44857498","https://openalex.org/W4383873717","https://openalex.org/W2062900651","https://openalex.org/W2007632118","https://openalex.org/W2147968878","https://openalex.org/W1982767103"],"abstract_inverted_index":{"We":[0],"solve":[1],"the":[2,11,14,18,24,52,55,60,71,75],"Boltzmann":[3],"equation,":[4],"whose":[5],"collision":[6,16,29,57,63],"term":[7,58],"is":[8,31,44,67,90],"modeled":[9],"by":[10,69],"hybridization":[12],"of":[13,26],"binary":[15,62],"and":[17,59,92],"BGK":[19],"approximation.":[20],"The":[21,65],"parameter":[22],"controlling":[23,70],"ratio":[25],"these":[27],"two":[28],"mechanisms":[30],"selected":[32],"adaptively":[33],"on":[34,46],"every":[35,39],"grid":[36],"cell":[37],"at":[38],"time":[40],"step.":[41],"This":[42],"self-adaptation":[43],"based":[45],"a":[47],"heuristic":[48],"error":[49,77,88],"indicator":[50,66,89],"describing":[51],"difference":[53],"between":[54],"model":[56],"original":[61],"term.":[64],"derived":[68],"quadratic":[72],"terms":[73],"in":[74],"modeling":[76],"with":[78],"linear":[79],"operators.":[80],"Our":[81],"numerical":[82],"experiments":[83],"show":[84],"that":[85],"such":[86],"an":[87],"effective":[91],"computationally":[93],"affordable.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
