{"id":"https://openalex.org/W4389194726","doi":"https://doi.org/10.3390/e25121609","title":"Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes","display_name":"Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes","publication_year":2023,"publication_date":"2023-11-30","ids":{"openalex":"https://openalex.org/W4389194726","doi":"https://doi.org/10.3390/e25121609","pmid":"https://pubmed.ncbi.nlm.nih.gov/38136489"},"language":"en","primary_location":{"id":"doi:10.3390/e25121609","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121609","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1609/pdf?version=1701404830","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/12/1609/pdf?version=1701404830","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102585846","display_name":"Linchang Han","orcid":null},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Linchang Han","raw_affiliation_strings":["Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"affiliations":[{"raw_affiliation_string":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008260778","display_name":"Liming Yang","orcid":"https://orcid.org/0000-0001-7961-4854"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]},{"id":"https://openalex.org/I890469752","display_name":"Ministry of Industry and Information Technology","ror":"https://ror.org/0385nmy68","country_code":"CN","type":"government","lineage":["https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liming Yang","raw_affiliation_strings":["Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing 210016, China","State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"affiliations":[{"raw_affiliation_string":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Key Laboratory of Unsteady Aerodynamics and Flow Control, Ministry of Industry and Information Technology, Nanjing 210016, China","institution_ids":["https://openalex.org/I890469752"]},{"raw_affiliation_string":"State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070632878","display_name":"Zhihui Li","orcid":"https://orcid.org/0000-0002-8378-6269"},"institutions":[{"id":"https://openalex.org/I2802505932","display_name":"China Aerodynamics Research and Development Center","ror":"https://ror.org/00jma8s40","country_code":"CN","type":"facility","lineage":["https://openalex.org/I2802505932"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihui Li","raw_affiliation_strings":["National Laboratory for Computational Fluid Dynamics, China Aerodynamics Research and Development Center, Beijing 100191, China"],"affiliations":[{"raw_affiliation_string":"National Laboratory for Computational Fluid Dynamics, China Aerodynamics Research and Development Center, Beijing 100191, China","institution_ids":["https://openalex.org/I2802505932"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046927354","display_name":"Jie Wu","orcid":"https://orcid.org/0000-0001-6963-0244"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Wu","raw_affiliation_strings":["Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"affiliations":[{"raw_affiliation_string":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102774700","display_name":"Yinjie Du","orcid":"https://orcid.org/0000-0001-9861-9490"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinjie Du","raw_affiliation_strings":["Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"affiliations":[{"raw_affiliation_string":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024672196","display_name":"Xiang Shen","orcid":"https://orcid.org/0000-0002-6696-1133"},"institutions":[{"id":"https://openalex.org/I32394136","display_name":"Northumbria University","ror":"https://ror.org/049e6bc10","country_code":"GB","type":"education","lineage":["https://openalex.org/I32394136"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xiang Shen","raw_affiliation_strings":["Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK","institution_ids":["https://openalex.org/I32394136"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5008260778","https://openalex.org/A5070632878"],"corresponding_institution_ids":["https://openalex.org/I2802505932","https://openalex.org/I890469752","https://openalex.org/I9842412"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5298,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63367389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"25","issue":"12","first_page":"1609","last_page":"1609"},"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":0.9998999834060669,"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":0.9994000196456909,"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/discretization","display_name":"Discretization","score":0.8820832967758179},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.8167901635169983},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5292325019836426},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5132780075073242},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.46602556109428406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42683202028274536},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.4221777319908142},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3818420171737671},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3577239513397217},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.32116448879241943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31665852665901184},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2879631519317627},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2793302536010742},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05554401874542236}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8820832967758179},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.8167901635169983},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5292325019836426},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5132780075073242},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.46602556109428406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42683202028274536},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.4221777319908142},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3818420171737671},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3577239513397217},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32116448879241943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31665852665901184},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2879631519317627},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2793302536010742},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05554401874542236},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e25121609","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121609","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1609/pdf?version=1701404830","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:38136489","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38136489","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10742583","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10742583","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10742583/pdf/entropy-25-01609.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:009d0e98e51844f0ae481cc3ec127595","is_oa":true,"landing_page_url":"https://doaj.org/article/009d0e98e51844f0ae481cc3ec127595","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 12, p 1609 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e25121609","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121609","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1609/pdf?version=1701404830","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1007721318","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320327518","funder_display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3910829908","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G4450908433","display_name":null,"funder_award_id":"BK2021","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G5131993150","display_name":null,"funder_award_id":"BK20210273","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6772616100","display_name":null,"funder_award_id":"12332013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G681149043","display_name":null,"funder_award_id":"12202191","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7342455266","display_name":null,"funder_award_id":"(PAPD)","funder_id":"https://openalex.org/F4320327518","funder_display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322438","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327518","display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389194726.pdf"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1538135945","https://openalex.org/W1964421235","https://openalex.org/W1976498611","https://openalex.org/W2008003005","https://openalex.org/W2013702974","https://openalex.org/W2021041911","https://openalex.org/W2034497250","https://openalex.org/W2038435678","https://openalex.org/W2042624429","https://openalex.org/W2053415457","https://openalex.org/W2062528395","https://openalex.org/W2066060292","https://openalex.org/W2080735958","https://openalex.org/W2083597099","https://openalex.org/W2086026333","https://openalex.org/W2087360755","https://openalex.org/W2089582312","https://openalex.org/W2090638504","https://openalex.org/W2093745494","https://openalex.org/W2106743858","https://openalex.org/W2112264486","https://openalex.org/W2138887979","https://openalex.org/W2309411886","https://openalex.org/W2343264068","https://openalex.org/W2471818076","https://openalex.org/W2485594073","https://openalex.org/W2522837359","https://openalex.org/W2728507037","https://openalex.org/W2746766329","https://openalex.org/W2769576272","https://openalex.org/W2916121615","https://openalex.org/W2936898908","https://openalex.org/W2954442294","https://openalex.org/W2975410448","https://openalex.org/W3012274752","https://openalex.org/W3046864439","https://openalex.org/W3101758090","https://openalex.org/W3105224026","https://openalex.org/W3160058050","https://openalex.org/W4211216527","https://openalex.org/W4241603153","https://openalex.org/W4251706365","https://openalex.org/W4283010297","https://openalex.org/W4293530520","https://openalex.org/W4313253246","https://openalex.org/W4384652028"],"related_works":["https://openalex.org/W4388257265","https://openalex.org/W849161923","https://openalex.org/W1579959893","https://openalex.org/W3404850","https://openalex.org/W4388401275","https://openalex.org/W4238782814","https://openalex.org/W4386916460","https://openalex.org/W58974396","https://openalex.org/W2484879441","https://openalex.org/W2055744950"],"abstract_inverted_index":{"How":[0],"to":[1,73,115,131,201,214],"improve":[2],"the":[3,25,40,44,49,71,75,82,91,108,121,125,133,149,166,170,175,179,184,194,202,209,215,221,228,233,237,256,259,263],"computational":[4,64,83,180,282],"efficiency":[5],"of":[6,43,51,87,107,120,148,165,174,182,193,205,232,247,258,262,272],"flow":[7,17,253],"field":[8],"simulations":[9],"around":[10,287],"irregular":[11,288],"objects":[12,289],"in":[13,24,58,62,77,124,138,208,220,236,249,279,290],"near-continuum":[14,252],"and":[15,54,99,140,251],"continuum":[16,250],"regimes":[18],"has":[19],"always":[20],"been":[21],"a":[22,35,161,281],"challenge":[23],"aerospace":[26],"re-entry":[27],"process.":[28],"The":[29],"discrete":[30,216],"velocity":[31,56,217],"method":[32],"(DVM)":[33],"is":[34,129,153,188,198],"commonly":[36],"used":[37],"algorithm":[38],"for":[39,169,284],"discretized":[41],"solutions":[42],"Boltzmann-BGK":[45,126,195,222,238],"model":[46],"equation.":[47,196,223],"However,":[48],"discretization":[50,119,173,231],"both":[52],"physical":[53],"molecular":[55],"spaces":[57],"DVM":[59,78,88,93,97,102,158,242],"can":[60,240],"result":[61],"significant":[63],"costs.":[65],"This":[66,197],"paper":[67],"focuses":[68],"on":[69],"unlocking":[70],"key":[72],"accelerate":[74,241],"convergence":[76],"calculations,":[79],"thereby":[80],"reducing":[81],"burden.":[84],"Three":[85],"versions":[86],"are":[89],"investigated:":[90],"semi-implicit":[92],"(DVM-I),":[94],"fully":[95,100,229],"implicit":[96,101,118,172,230],"(DVM-II),":[98],"with":[103],"an":[104,144,268],"inner":[105,145,260],"iteration":[106,261],"macroscopic":[109,135,150,185,210,264],"governing":[110,136,151,186,211,265],"equation":[111,137,152,187,212,239,266],"(DVM-III).":[112],"In":[113,142],"order":[114,246],"achieve":[116],"full":[117,171],"collision":[122,176,234],"term":[123,235],"equation,":[127],"it":[128],"necessary":[130],"solve":[132],"corresponding":[134],"DVM-II":[139],"DVM-III.":[141],"DVM-III,":[143],"iterative":[146],"process":[147],"employed":[154],"between":[155],"two":[156],"adjacent":[157],"steps,":[159],"enabling":[160],"more":[162],"accurate":[163],"prediction":[164],"equilibrium":[167],"state":[168],"term.":[177],"Fortunately,":[178],"cost":[181],"solving":[183],"significantly":[189],"lower":[190],"than":[191],"that":[192,227],"primarily":[199],"due":[200],"smaller":[203],"number":[204],"conservative":[206],"variables":[207],"compared":[213],"distribution":[218],"functions":[219],"Our":[224],"findings":[225],"demonstrate":[226],"calculations":[243],"by":[244],"one":[245],"magnitude":[248,273],"regimes.":[254],"Furthermore,":[255],"introduction":[257],"provides":[267],"additional":[269],"1-2":[270],"orders":[271],"acceleration.":[274],"Such":[275],"advancements":[276],"hold":[277],"promise":[278],"providing":[280],"approach":[283],"simulating":[285],"flows":[286],"near-space":[291],"environments.":[292]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}