{"id":"https://openalex.org/W7216340393","doi":"https://doi.org/10.48550/arxiv.2610.00811","title":"A relaxation system for the low-Mach limit of kinetic equations: Stability and higher order asymptotic preserving scheme","display_name":"A relaxation system for the low-Mach limit of kinetic equations: Stability and higher order asymptotic preserving scheme","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7216340393","doi":"https://doi.org/10.48550/arxiv.2610.00811"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00811","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00811","pdf_url":"https://arxiv.org/pdf/2610.00811","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.00811","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035852692","display_name":"Giacomo Dimarco","orcid":"https://orcid.org/0000-0001-6186-3633","observed_orcids":["https://orcid.org/0000-0001-6186-3633"]},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dimarco, Giacomo","raw_affiliation_strings":["Center for Modeling, Computing and Statistics , University of Ferrara , Italy","Department of Mathematics and Computer Science , University of Ferrara , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Modeling, Computing and Statistics , University of Ferrara , Italy","institution_ids":["https://openalex.org/I201324441"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of Ferrara , Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058610061","display_name":"Axel Klar","orcid":"https://orcid.org/0000-0003-1679-9438","observed_orcids":["https://orcid.org/0000-0003-1679-9438"]},"institutions":[{"id":"https://openalex.org/I4387152675","display_name":"Rheinland-Pf\u00e4lzische Technische Universit\u00e4t Kaiserslautern-Landau","ror":"https://ror.org/01qrts582","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387152675"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klar, Axel","raw_affiliation_strings":["Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE","institution_ids":["https://openalex.org/I4387152675"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121291589","display_name":"Theresa K\u00f6fler","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I4387152675","display_name":"Rheinland-Pf\u00e4lzische Technische Universit\u00e4t Kaiserslautern-Landau","ror":"https://ror.org/01qrts582","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387152675"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"K\u00f6fler, Theresa","raw_affiliation_strings":["Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE","Department of Mathematics and Computer Science , University of Ferrara , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE","institution_ids":["https://openalex.org/I4387152675"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of Ferrara , Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009401094","display_name":"Lorenzo Pareschi","orcid":"https://orcid.org/0000-0002-8706-6939","observed_orcids":["https://orcid.org/0000-0002-8706-6939"]},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Pareschi, Lorenzo","raw_affiliation_strings":["Department of Mathematics and Computer Science , University of Ferrara , Italy","Maxwell Institute for Mathematical Sciences and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of Ferrara , Italy","institution_ids":["https://openalex.org/I201324441"]},{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences and","institution_ids":["https://openalex.org/I4210117017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111432613","display_name":"Sudarshan Tiwari","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]},{"id":"https://openalex.org/I4387152675","display_name":"Rheinland-Pf\u00e4lzische Technische Universit\u00e4t Kaiserslautern-Landau","ror":"https://ror.org/01qrts582","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387152675"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Tiwari, Sudarshan","raw_affiliation_strings":["Department of Mathematics , Heriot-Watt University , Edinburgh , UK","Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Heriot-Watt University , Edinburgh , UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"Department of Mathematics , RPTU Kaiserslautern-Landau , Kaiserslautern , DE","institution_ids":["https://openalex.org/I4387152675"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5128417427","display_name":"Yizhou Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Zhou, Yizhou","raw_affiliation_strings":["Department of Mathematics , RWTH Aachen , Aachen , DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , RWTH Aachen , Aachen , DE","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9092000126838684,"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":0.9092000126838684,"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":0.08219999819993973,"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":0.0013000000035390258,"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/low-mach-number-limit","display_name":"low Mach number limit","score":0.8159999847412109},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.9879999756813049},{"id":"https://openalex.org/keywords/bgk-model","display_name":"BGK model","score":0.8399999737739563},{"id":"https://openalex.org/keywords/micro-macro-decomposition","display_name":"micro-macro decomposition","score":0.9900000095367432},{"id":"https://openalex.org/keywords/asymptotic-preserving-schemes","display_name":"asymptotic preserving schemes","score":0.7319999933242798},{"id":"https://openalex.org/keywords/structural-stability","display_name":"structural stability","score":0.8059999942779541},{"id":"https://openalex.org/keywords/weno-schemes","display_name":"WENO schemes","score":0.5370000004768372},{"id":"https://openalex.org/keywords/knudsen-number","display_name":"Knudsen number","score":0.7699999809265137},{"id":"https://openalex.org/keywords/high-order-discretization","display_name":"high-order discretization","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.644599974155426},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5805000066757202},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.49070000648498535},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47859999537467957},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4374000132083893},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4244999885559082},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C165231844","wikidata":"https://www.wikidata.org/wiki/Q160669","display_name":"Mach number","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2863999903202057},{"id":"https://openalex.org/C121838276","wikidata":"https://www.wikidata.org/wiki/Q898463","display_name":"Knudsen number","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C2235679","wikidata":"https://www.wikidata.org/wiki/Q6410797","display_name":"Kinetic scheme","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2533000111579895},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00811","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00811","pdf_url":"https://arxiv.org/pdf/2610.00811","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2610.00811","doi":"https://doi.org/10.48550/arxiv.2610.00811","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00811","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.00811","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00811","pdf_url":"https://arxiv.org/pdf/2610.00811","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216340393.pdf","grobid_xml":"https://content.openalex.org/works/W7216340393.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7166590569","https://openalex.org/W7167901924"],"related_works":["https://openalex.org/W2051680717","https://openalex.org/W7166590569","https://openalex.org/W7099739099","https://openalex.org/W2230934360","https://openalex.org/W1978434425","https://openalex.org/W7117257450","https://openalex.org/W1667376670","https://openalex.org/W7202122213","https://openalex.org/W2029987438","https://openalex.org/W2079218650"],"abstract_inverted_index":{"This":[0],"work":[1],"introduces":[2],"a":[3,24,39,44,49,59,66,75,83,88,109,156,193],"hyperbolic":[4,85],"relaxation":[5,69,89],"system":[6,41,73,81],"designed":[7],"for":[8,122,136],"the":[9,15,28,34,55,92,97,102,162,168,180],"simulation":[10],"of":[11,27,43,61,77,161,196],"kinetic":[12,35],"equations":[13],"in":[14,101,174,186],"low-Mach":[16],"number":[17],"limit.":[18,94,105],"The":[19,71,141],"methodology":[20],"is":[21,74],"built":[22],"upon":[23],"micro-macro":[25],"decomposition":[26],"scaled":[29],"BGK":[30],"model,":[31],"which":[32],"reformulates":[33],"distribution":[36],"function":[37],"into":[38,155],"coupled":[40],"consisting":[42],"macroscopic":[45],"equilibrium":[46],"part":[47,86],"and":[48,87,125,147,176,189,198],"microscopic":[50,56],"non-equilibrium":[51],"remainder.":[52],"By":[53],"projecting":[54],"deviations":[57],"onto":[58],"set":[60],"orthogonal":[62],"polynomials,":[63],"we":[64,107],"derive":[65],"closed":[67],"moment":[68,80],"system.":[70],"resulting":[72],"version":[76],"Grad's":[78],"13":[79],"with":[82],"linear":[84],"adapted":[90],"to":[91],"incompressible":[93,103,163],"We":[95],"prove":[96],"model's":[98],"structural":[99],"stability":[100,146],"Navier-Stokes":[104,165],"Moreover,":[106],"develop":[108],"high":[110,137,158],"order":[111,138,159],"Asymptotic-Preserving":[112],"(AP)":[113],"numerical":[114],"framework":[115],"using":[116],"Implicit-Explicit":[117],"(IMEX)":[118],"Runge":[119],"Kutta":[120],"schemes":[121],"temporal":[123],"accuracy":[124],"finite":[126],"difference":[127,134],"WENO":[128],"reconstructions":[129],"as":[130,132,167],"well":[131],"central":[133],"approximations":[135],"spatial":[139],"resolution.":[140],"proposed":[142],"scheme":[143],"ensures":[144],"uniform":[145],"consistency":[148],"across":[149,192],"different":[150],"physical":[151],"regimes,":[152],"automatically":[153],"degenerating":[154],"consistent":[157],"discretization":[160],"thermal":[164],"limit":[166],"scaling":[169],"parameter":[170],"vanishes.":[171],"Numerical":[172],"experiments":[173],"one":[175],"two":[177],"dimensions":[178],"corroborate":[179],"theoretical":[181],"findings,":[182],"demonstrating":[183],"significant":[184],"reductions":[185],"computational":[187],"cost":[188],"robust":[190],"performance":[191],"wide":[194],"range":[195],"Knudsen":[197],"Mach":[199],"numbers.":[200]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
