{"id":"https://openalex.org/W7128607238","doi":"https://doi.org/10.48550/arxiv.2602.09077","title":"Fixed-grid sharp-interface numerical solutions to the three-phase spherical Stefan problem","display_name":"Fixed-grid sharp-interface numerical solutions to the three-phase spherical Stefan problem","publication_year":2026,"publication_date":"2026-02-09","ids":{"openalex":"https://openalex.org/W7128607238","doi":"https://doi.org/10.48550/arxiv.2602.09077"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.09077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09077","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.09077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125671419","display_name":"Yavkreet Swami","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Swami, Yavkreet","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125664479","display_name":"Jacob Barajas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barajas, Jacob","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073320735","display_name":"Amneet Pal Singh Bhalla","orcid":"https://orcid.org/0000-0002-0173-9881"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhalla, Amneet Pal Singh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10938","display_name":"Phase Change Materials Research","score":0.7340999841690063,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T10938","display_name":"Phase Change Materials Research","score":0.7340999841690063,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.09229999780654907,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.06840000301599503,"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/stefan-problem","display_name":"Stefan problem","score":0.9333999752998352},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.6254000067710876},{"id":"https://openalex.org/keywords/phase-change","display_name":"Phase change","score":0.527899980545044},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4788999855518341},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42149999737739563},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41119998693466187},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.3930000066757202},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.388700008392334},{"id":"https://openalex.org/keywords/boiling","display_name":"Boiling","score":0.38029998540878296}],"concepts":[{"id":"https://openalex.org/C2778021227","wikidata":"https://www.wikidata.org/wiki/Q3775789","display_name":"Stefan problem","level":3,"score":0.9333999752998352},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.6254000067710876},{"id":"https://openalex.org/C133256868","wikidata":"https://www.wikidata.org/wiki/Q7180940","display_name":"Phase change","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4788999855518341},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.40450000762939453},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3856000006198883},{"id":"https://openalex.org/C157777378","wikidata":"https://www.wikidata.org/wiki/Q41716","display_name":"Boiling","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37770000100135803},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C200093464","wikidata":"https://www.wikidata.org/wiki/Q166583","display_name":"Condensation","level":2,"score":0.3292999863624573},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C144308804","wikidata":"https://www.wikidata.org/wiki/Q232997","display_name":"Two-phase flow","level":3,"score":0.3122999966144562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31130000948905945},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29260000586509705},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C2778119658","wikidata":"https://www.wikidata.org/wiki/Q1806889","display_name":"Phase-change material","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2773999869823456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26989999413490295},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.2606000006198883},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.09077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09077","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.09077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09077","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"metal":[1],"manufacturing":[2],"processes":[3],"involve":[4],"phase":[5,26,57,73,253],"change":[6,27,58,74,254],"phenomena,":[7],"which":[8,159],"include":[9],"melting,":[10,109],"boiling,":[11,111],"and":[12,97,112,155,208,211,268],"vaporization.":[13],"These":[14],"phenomena":[15,28],"often":[16],"occur":[17],"concurrently.":[18],"A":[19],"prototypical":[20],"1D":[21],"model":[22],"for":[23,138,174,264],"understanding":[24],"the":[25,30,41,45,52,79,83,86,101,131,149,152,156,164,179,205,214,217,226,239,246],"is":[29,34,160,222],"Stefan":[31,47,87,103,133,241],"problem.":[32,88],"There":[33,141],"a":[35,127,183,192,198],"large":[36,265],"body":[37],"of":[38,56,85,108,202,216,231,248,255],"literature":[39,80],"discussing":[40],"analytical":[42,96,168,194],"solution":[43,169],"to":[44,81,100,125,244],"two-phase":[46,227],"problem":[48,104,134],"that":[49,67],"describes":[50],"only":[51],"melting":[53,229],"or":[54],"boiling":[55,153],"materials":[59],"(PCMs)":[60],"with":[61,105,163,187],"one":[62],"moving":[63,144],"interface.":[64],"Density-change":[65],"effects":[66,262],"induce":[68],"additional":[69],"fluid":[70],"flow":[71],"during":[72,252],"are":[75,142],"generally":[76],"neglected":[77],"in":[78,114,135,146,161],"simplify":[82],"math":[84],"In":[89,259],"our":[90,122],"recent":[91],"work":[92,119,124],"[1],":[93],"we":[94,177,196,237],"provide":[95],"numerical":[98,220],"solutions":[99],"three-phase":[102,132,240],"simultaneous":[106],"occurrences":[107],"solidification,":[110],"condensation":[113],"Cartesian":[115],"coordinates.":[116],"Our":[117,219],"current":[118],"builds":[120],"on":[121],"previous":[123],"solve":[126,238],"more":[128],"challenging":[129],"problem:":[130],"spherical":[136],"coordinates":[137],"finite-sized":[139],"particles.":[140,258],"three":[143,206],"interfaces":[145],"this":[147,175],"system:":[148],"melt":[150],"front,":[151,154],"outer":[157],"boundary":[158],"contact":[162],"atmosphere.":[165],"Although":[166],"an":[167],"could":[170],"not":[171],"be":[172],"found":[173],"problem,":[176],"solved":[178],"governing":[180],"equations":[181],"using":[182],"fixed-grid":[184],"sharp-interface":[185],"method":[186,221],"second-order":[188],"spatio-temporal":[189],"accuracy.":[190],"Using":[191],"small-time":[193],"solution,":[195],"predict":[197],"reasonably":[199],"accurate":[200],"estimate":[201],"temperature":[203],"(in":[204],"phases)":[207],"interface":[209],"positions":[210],"velocities":[212],"at":[213],"start":[215],"simulation.":[218],"validated":[223],"by":[224],"reproducing":[225],"nanoparticle":[228],"results":[230],"Font":[232],"et":[233],"al.":[234],"[2].":[235],"Lastly,":[236],"problems":[242],"numerically":[243],"demonstrate":[245],"importance":[247],"kinetic":[249],"energy":[250],"terms":[251],"smaller":[256],"(nano)":[257],"contrast,":[260],"these":[261],"diminish":[263],"particles":[266],"(microns":[267],"larger).":[269]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-02-12T00:00:00"}
