{"id":"https://openalex.org/W7214967293","doi":"https://doi.org/10.48550/arxiv.2609.35989","title":"Divergence-free magnetohydrodynamics on a moving mesh","display_name":"Divergence-free magnetohydrodynamics on a moving mesh","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214967293","doi":"https://doi.org/10.48550/arxiv.2609.35989"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35989","pdf_url":"https://arxiv.org/pdf/2609.35989","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/2609.35989","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004531924","display_name":"Volker Springel","orcid":"https://orcid.org/0000-0001-5976-4599","observed_orcids":["https://orcid.org/0000-0001-5976-4599"]},"institutions":[{"id":"https://openalex.org/I4210103661","display_name":"Max Planck Institute for Astrophysics","ror":"https://ror.org/017qcv467","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210103661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Springel, Volker","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany","institution_ids":["https://openalex.org/I4210103661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108871990","display_name":"Alexander C. Mayer","orcid":"https://orcid.org/0000-0002-1405-9914","observed_orcids":["https://orcid.org/0000-0002-1405-9914"]},"institutions":[{"id":"https://openalex.org/I4210103661","display_name":"Max Planck Institute for Astrophysics","ror":"https://ror.org/017qcv467","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210103661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mayer, Alexander C.","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany","institution_ids":["https://openalex.org/I4210103661"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153647989","display_name":"R\u00fcdiger Pakmor","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210103661","display_name":"Max Planck Institute for Astrophysics","ror":"https://ror.org/017qcv467","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210103661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pakmor, R\u00fcdiger","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Astrophysik , Karl-Schwarzschild-Str. 1 , D-85748 , Garching , Germany","institution_ids":["https://openalex.org/I4210103661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210103661"],"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9452999830245972,"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":0.9452999830245972,"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/T10477","display_name":"Astrophysics and Star Formation Studies","score":0.014700000174343586,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.010200000368058681,"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/magnetic-vector-potential","display_name":"vector potential","score":0.7080000042915344},{"id":"https://openalex.org/keywords/moving-mesh-method","display_name":"moving mesh","score":0.7409999966621399},{"id":"https://openalex.org/keywords/galilean-invariance","display_name":"Galilean invariance","score":0.9539999961853027},{"id":"https://openalex.org/keywords/lagrangian-hydrodynamics","display_name":"Lagrangian hydrodynamics","score":0.7829999923706055},{"id":"https://openalex.org/keywords/arepo","display_name":"AREPO","score":0.7350000143051147},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"adaptive mesh refinement","score":0.953000009059906},{"id":"https://openalex.org/keywords/ideal-mhd-stability","display_name":"ideal MHD stability","score":0.5360000133514404}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.786899983882904},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.7416999936103821},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6075999736785889},{"id":"https://openalex.org/C74797697","wikidata":"https://www.wikidata.org/wiki/Q2481895","display_name":"Galilean invariance","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C2776442084","wikidata":"https://www.wikidata.org/wiki/Q5518599","display_name":"Galilean","level":2,"score":0.5357999801635742},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.49630001187324524},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4262000024318695},{"id":"https://openalex.org/C194127275","wikidata":"https://www.wikidata.org/wiki/Q92795812","display_name":"Magnetic potential","level":3,"score":0.4187999963760376},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4146000146865845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3944999873638153},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3612000048160553},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.35670000314712524},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.34369999170303345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30160000920295715},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2996000051498413},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28850001096725464},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26809999346733093}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35989","pdf_url":"https://arxiv.org/pdf/2609.35989","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.2609.35989","doi":"https://doi.org/10.48550/arxiv.2609.35989","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35989","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:2609.35989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35989","pdf_url":"https://arxiv.org/pdf/2609.35989","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214967293.pdf","grobid_xml":"https://content.openalex.org/works/W7214967293.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4210314528","https://openalex.org/W4382490902","https://openalex.org/W7166526429","https://openalex.org/W7167799950","https://openalex.org/W7172440977","https://openalex.org/W7202135443"],"related_works":["https://openalex.org/W2902588427","https://openalex.org/W1816752383","https://openalex.org/W7098740525","https://openalex.org/W4221154658","https://openalex.org/W1862463322","https://openalex.org/W1990511060","https://openalex.org/W2586161487","https://openalex.org/W2014417457","https://openalex.org/W2104377728","https://openalex.org/W1872855437"],"abstract_inverted_index":{"Magnetic":[0],"fields":[1],"are":[2,34,73,227],"ubiquitous":[3],"in":[4,12,59,74,99,171,215],"the":[5,21,38,52,60,110,113,118,164,172],"Universe":[6],"and":[7,20,44,125,142,168,183,200,211,221,225],"play":[8],"an":[9,104,122],"important":[10],"role":[11],"many":[13],"astrophysical":[14],"processes,":[15],"such":[16,191],"as":[17,192],"star":[18],"formation":[19],"evolution":[22,152],"of":[23,54,92,112,145,153,163],"galaxies.":[24],"Hydrodynamical":[25],"simulation":[26],"methods":[27],"that":[28,94],"account":[29],"for":[30,116,188],"ideal":[31],"magnetohydrodynamics":[32],"(MHD)":[33],"however":[35],"challenged":[36],"by":[37,51],"need":[39],"to":[40,65,207,212],"achieve":[41],"numerical":[42],"stability":[43,201],"physical":[45],"consistency.":[46],"Both":[47],"can":[48,95],"be":[49,96],"compromised":[50],"occurrence":[53],"non-vanishing":[55],"local":[56,219],"divergence":[57,81],"errors":[58,72,187],"magnetic":[61,119],"field.":[62],"Different":[63],"approaches":[64],"either":[66],"eliminate":[67],"or":[68,80],"reduce":[69],"these":[70],"discretization":[71],"widespread":[75],"use,":[76],"including":[77,217],"constrained":[78],"transport":[79],"cleaning":[82],"techniques.":[83],"However,":[84],"thus":[85],"far":[86],"a":[87,128,134,140,150,154,159],"divergence-free":[88],"Galilean":[89,181],"invariant":[90,182],"formulation":[91,144],"MHD":[93],"readily":[97],"applied":[98,206],"Lagrangian":[100],"codes":[101],"has":[102],"been":[103],"elusive":[105],"goal.":[106],"Here":[107],"we":[108],"revisit":[109],"use":[111],"vector":[114,156],"potential":[115,157],"evolving":[117],"field":[120,193],"on":[121],"unstructured":[123],"moving-mesh":[124,173],"show":[126],"how":[127],"particular":[129],"gauge":[130],"choice":[131],"combined":[132],"with":[133,158],"suitably":[135],"discretized":[136],"integration":[137],"scheme":[138,204],"provides":[139],"stable":[141],"accurate":[143],"MHD.":[146],"Our":[147],"method":[148],"combines":[149],"finite-difference":[151],"cell-centred":[155],"finite":[160],"volume":[161],"representation":[162],"other":[165],"fluid":[166],"quantities,":[167],"is":[169,179,205],"realized":[170],"code":[174],"AREPO.":[175],"The":[176],"new":[177],"approach":[178],"fully":[180],"therefore":[184],"shows":[185],"vanishing":[186],"classic":[189],"problems":[190,210],"loop":[194],"advection.":[195],"We":[196],"demonstrate":[197],"good":[198],"accuracy":[199],"when":[202,218],"our":[203],"various":[208],"test":[209],"practical":[213],"applications":[214],"3D,":[216],"timesteps":[220],"adaptive":[222],"mesh":[223],"refinement":[224],"derefinement":[226],"used.":[228]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
