{"id":"https://openalex.org/W2080626180","doi":"https://doi.org/10.1515/jnma-2014-0006","title":"Fully implicit nonstationary flow simulations with a monolithic off-lattice Boltzmann approach","display_name":"Fully implicit nonstationary flow simulations with a monolithic off-lattice Boltzmann approach","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2080626180","doi":"https://doi.org/10.1515/jnma-2014-0006","mag":"2080626180"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2014-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2014-0006","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical 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/A5020658676","display_name":"Thomas H\u00fcbner","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I300951488","display_name":"Higher Education Commission","ror":"https://ror.org/038y3sz68","country_code":"PK","type":"government","lineage":["https://openalex.org/I300951488"]}],"countries":["DE","PK"],"is_corresponding":false,"raw_author_name":"T. H\u00fcbner","raw_affiliation_strings":["Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan","institution_ids":["https://openalex.org/I300951488","https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091116292","display_name":"Rashid Mahmood","orcid":"https://orcid.org/0000-0002-0591-7753"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I300951488","display_name":"Higher Education Commission","ror":"https://ror.org/038y3sz68","country_code":"PK","type":"government","lineage":["https://openalex.org/I300951488"]}],"countries":["DE","PK"],"is_corresponding":false,"raw_author_name":"R. Mahmood","raw_affiliation_strings":["Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan","institution_ids":["https://openalex.org/I300951488","https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059837563","display_name":"Stefan Turek","orcid":"https://orcid.org/0000-0002-9740-6087"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I300951488","display_name":"Higher Education Commission","ror":"https://ror.org/038y3sz68","country_code":"PK","type":"government","lineage":["https://openalex.org/I300951488"]}],"countries":["DE","PK"],"is_corresponding":false,"raw_author_name":"S. Turek","raw_affiliation_strings":["Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics, TU Dortmund, Germany. This work is kindly supported by the BMBF (SKALB project, grant 01IH08003D) and the Higher Education Commission (HEC) of Pakistan","institution_ids":["https://openalex.org/I300951488","https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12329327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","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"}},"topics":[{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","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/T12163","display_name":"Aerosol Filtration and Electrostatic Precipitation","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9886999726295471,"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":0.795306384563446},{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.6682934165000916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6670169830322266},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.636296808719635},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5341194272041321},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5259243249893188},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47843697667121887},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.46993809938430786},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.46569690108299255},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4611722528934479},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.4376160204410553},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38807910680770874},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3660770058631897},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27415263652801514},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16704332828521729},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.09621423482894897}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.795306384563446},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.6682934165000916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6670169830322266},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.636296808719635},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5341194272041321},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5259243249893188},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47843697667121887},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.46993809938430786},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.46569690108299255},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4611722528934479},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.4376160204410553},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38807910680770874},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3660770058631897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27415263652801514},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16704332828521729},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.09621423482894897},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2014-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2014-0006","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W1537807642","https://openalex.org/W44857498","https://openalex.org/W2062900651","https://openalex.org/W2147968878","https://openalex.org/W2019645917","https://openalex.org/W1982767103"],"abstract_inverted_index":{"In":[0,20],"this":[1],"paper,":[2],"the":[3,10,35,53,73,83,106,111,118,126,132,136,154,158,162,175],"previously":[4],"described":[5],"monolithic":[6],"approach":[7],"[6]":[8],"for":[9,45,69,82,140,153,181],"stationary":[11],"discrete":[12],"Boltzmann":[13,38],"equation":[14],"is":[15,63,122],"extended":[16],"to":[17,34,99,125,144],"time-dependent":[18],"problems.":[19,56],"general,":[21],"both":[22],"collision":[23],"and":[24,48,167,172],"advection":[25],"operators":[26,116,138],"are":[27,43,151,179],"discretized":[28],"on":[29,161],"nonuniform":[30],"grids":[31],"as":[32],"opposed":[33],"standard":[36],"Lattice":[37],"method.":[39],"Implicit":[40],"time-stepping":[41],"schemes":[42,94],"applied":[44,119],"an":[46],"accurate":[47],"robust":[49],"numerical":[50,67],"treatment":[51],"of":[52,61,92,96,105,113,135,174],"nonstationary":[54],"flow":[55,183],"The":[57,103],"resulting":[58],"coupled":[59],"system":[60],"equations":[62],"treated":[64],"using":[65],"special":[66,146],"methods":[68],"PDE\u2019s.":[70],"As":[71],"in":[72,117],"steady":[74],"case,":[75],"we":[76,87],"apply":[77],"a":[78,145],"full":[79],"Newton":[80],"method":[81],"nonlinear":[84],"problems,":[85],"but":[86],"also":[88],"discuss":[89],"possible":[90],"variants":[91],"semi-implicit":[93],"all":[95],"which":[97],"lead":[98],"nonsymmetric":[100],"linear":[101],"systems.":[102],"preconditioning":[104],"used":[107],"Krylov-space":[108],"methods,":[109],"resp.,":[110],"construction":[112],"corresponding":[114],"smoothing":[115],"multigrid":[120],"approaches":[121],"closely":[123],"connected":[124],"underlying":[127],"short":[128],"characteristic-upwinding":[129],"discretization,":[130],"yielding":[131],"exact":[133],"inverse":[134],"transport":[137],"even":[139],"unstructured":[141],"meshes":[142],"due":[143],"numbering":[147],"technique.":[148],"Numerical":[149],"results":[150],"given":[152],"proposed":[155],"solvers":[156],"analysing":[157],"efficiency":[159],"depending":[160],"Mach":[163],"number,":[164],"time":[165],"step":[166],"mesh":[168],"size,":[169],"while":[170],"accuracy":[171],"stability":[173],"complete":[176],"space-time":[177],"discretization":[178],"demonstrated":[180],"prototypical":[182],"configurations":[184],"at":[185],"various":[186],"timesteps.":[187]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
