{"id":"https://openalex.org/W2888773888","doi":"https://doi.org/10.1137/18m1172533","title":"Computation of a Shrinking Interface in a Hele-Shaw Cell","display_name":"Computation of a Shrinking Interface in a Hele-Shaw Cell","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2888773888","doi":"https://doi.org/10.1137/18m1172533","mag":"2888773888"},"language":"en","primary_location":{"id":"doi:10.1137/18m1172533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1172533","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5068466448","display_name":"Meng Zhao","orcid":"https://orcid.org/0000-0002-0130-7333"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Meng Zhao","raw_affiliation_strings":["Illinois Institute of Technology; University of California at Irvine"],"affiliations":[{"raw_affiliation_string":"Illinois Institute of Technology; University of California at Irvine","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100637079","display_name":"Xiaofan Li","orcid":"https://orcid.org/0000-0001-9571-7482"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaofan Li","raw_affiliation_strings":["Illinois Institute of technology"],"affiliations":[{"raw_affiliation_string":"Illinois Institute of technology","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018844316","display_name":"Wenjun Ying","orcid":"https://orcid.org/0000-0002-8038-9372"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjun Ying","raw_affiliation_strings":["Shanghai Jiao Tong University"],"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079415900","display_name":"Andrew Belmonte","orcid":"https://orcid.org/0000-0002-2465-4629"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Belmonte","raw_affiliation_strings":["Mathematics"],"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010714351","display_name":"John Lowengrub","orcid":"https://orcid.org/0000-0003-1759-0900"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Lowengrub","raw_affiliation_strings":["University of California at Irvine"],"affiliations":[{"raw_affiliation_string":"University of California at Irvine","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052374499","display_name":"Shuwang Li","orcid":"https://orcid.org/0000-0002-4982-6650"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuwang Li","raw_affiliation_strings":["Illinois Institute of technology"],"affiliations":[{"raw_affiliation_string":"Illinois Institute of technology","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5068466448"],"corresponding_institution_ids":["https://openalex.org/I180949307"],"apc_list":null,"apc_paid":null,"fwci":1.8467,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86244678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"40","issue":"4","first_page":"B1206","last_page":"B1228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.978600025177002,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6160183548927307},{"id":"https://openalex.org/keywords/hele-shaw-flow","display_name":"Hele-Shaw flow","score":0.49384957551956177},{"id":"https://openalex.org/keywords/viscous-fingering","display_name":"Viscous fingering","score":0.4787984788417816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47519147396087646},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4615635275840759},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.456545352935791},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43956267833709717},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.37620049715042114},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28754737973213196},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.23795375227928162},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15030130743980408},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1329474151134491},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.13207343220710754}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6160183548927307},{"id":"https://openalex.org/C45502583","wikidata":"https://www.wikidata.org/wiki/Q5701708","display_name":"Hele-Shaw flow","level":4,"score":0.49384957551956177},{"id":"https://openalex.org/C2778737968","wikidata":"https://www.wikidata.org/wiki/Q3027832","display_name":"Viscous fingering","level":4,"score":0.4787984788417816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47519147396087646},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4615635275840759},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.456545352935791},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43956267833709717},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.37620049715042114},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28754737973213196},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.23795375227928162},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15030130743980408},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1329474151134491},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.13207343220710754},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1172533","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1172533","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1634719776","display_name":null,"funder_award_id":"P50GM76516","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G4178773435","display_name":null,"funder_award_id":"DMS-11771290","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4651208015","display_name":null,"funder_award_id":"DMS-1719960","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5445820216","display_name":null,"funder_award_id":"ECCS-1307625","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8420559147","display_name":null,"funder_award_id":"DMS-1720420","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1967318251","https://openalex.org/W1971163433","https://openalex.org/W1972080558","https://openalex.org/W1974133783","https://openalex.org/W1975454348","https://openalex.org/W1977120733","https://openalex.org/W1982959283","https://openalex.org/W1988264778","https://openalex.org/W2000251948","https://openalex.org/W2009275326","https://openalex.org/W2010085131","https://openalex.org/W2010142977","https://openalex.org/W2012882373","https://openalex.org/W2013776667","https://openalex.org/W2017791617","https://openalex.org/W2019390472","https://openalex.org/W2025739397","https://openalex.org/W2030510871","https://openalex.org/W2036667275","https://openalex.org/W2038546765","https://openalex.org/W2040228611","https://openalex.org/W2041170998","https://openalex.org/W2048285539","https://openalex.org/W2049155959","https://openalex.org/W2050196622","https://openalex.org/W2051548862","https://openalex.org/W2054497109","https://openalex.org/W2054864622","https://openalex.org/W2068650486","https://openalex.org/W2073560536","https://openalex.org/W2077037953","https://openalex.org/W2082306300","https://openalex.org/W2083206954","https://openalex.org/W2086692789","https://openalex.org/W2088791230","https://openalex.org/W2095257792","https://openalex.org/W2115269477","https://openalex.org/W2125782398","https://openalex.org/W2140153041","https://openalex.org/W2161265995","https://openalex.org/W2175659469","https://openalex.org/W2218684725","https://openalex.org/W2317132829","https://openalex.org/W2323238509","https://openalex.org/W2324263776","https://openalex.org/W2331828104","https://openalex.org/W2586353034"],"related_works":["https://openalex.org/W2039699594","https://openalex.org/W4322744399","https://openalex.org/W4308572070","https://openalex.org/W2613929631","https://openalex.org/W1967091491","https://openalex.org/W2753224743","https://openalex.org/W2593135060","https://openalex.org/W2619841764","https://openalex.org/W2091667337","https://openalex.org/W4322763587"],"abstract_inverted_index":{"In":[0,142,249],"this":[1],"paper,":[2],"we":[3,74,124,233,251],"present":[4],"an":[5],"adaptive":[6],"rescaling":[7,139],"method":[8,131,207],"for":[9,165,217],"computing":[10],"a":[11,15,19,30,36,76,89,96,114,126,134,275],"shrinking":[12,85,182],"interface":[13,122,150,160,183,227,263,293,306],"in":[14,132,259,313],"Hele-Shaw":[16,33],"cell":[17],"with":[18,238],"time":[20,136],"increasing":[21],"gap":[22,48,69,79,108,221,247,281],"width":[23],"b(t).":[24,70],"We":[25,213],"focus":[26],"our":[27,285],"study":[28],"on":[29,64],"one-phase":[31],"interior":[32],"problem":[34],"where":[35,99],"blob":[37],"of":[38,67,104,148,220,241],"fluid,":[39],"surrounded":[40],"by":[41,158,179],"air,":[42],"dynamically":[43],"responds":[44],"to":[45,111,171,193],"the":[46,65,68,102,105,119,143,146,149,155,159,166,174,180,191,206,225,239,245,255,261,292,305,314,318],"changing":[47],"width.":[49,248],"Linear":[50],"analysis":[51],"suggests":[52],"that":[53,82,205,253,288,300],"there":[54,309],"exist":[55],"transient":[56,226,265],"fingering":[57,97],"instabilities":[58,270],"and":[59,137,188,211,266],"noncircular":[60],"self-similar":[61],"evolutions":[62],"depending":[63],"dynamics":[66,192,219,228],"Using":[71],"linear":[72,242],"theory,":[73],"identify":[75],"critical":[77,246],"dynamic":[78],"thickness":[80],"b_c_k(t)":[81],"separates":[83],"stable":[84],"behavior":[86,235],"(shrinkage":[87,94],"like":[88,95],"circle)":[90],"from":[91],"unstable":[92],"shrinkage":[93],"pattern),":[98],"k":[100],"is":[101,140,151,208,320],"wavenumber":[103],"perturbation.":[106],"The":[107],"b_c_k":[109],"tends":[110],"infinity":[112],"at":[113,185,289],"finite":[115],"time.":[116],"To":[117],"explore":[118],"full":[120],"nonlinear":[121,215,262,315],"dynamics,":[123],"develop":[125],"spectrally":[127],"accurate":[128],"boundary":[129],"integral":[130],"which":[133],"new":[135],"space":[138],"implemented.":[141],"rescaled":[144],"frame,":[145],"motion":[147],"slowed":[152],"down,":[153],"while":[154,224],"area/volume":[156],"enclosed":[157],"remains":[161],"unchanged.":[162],"This":[163],"method,":[164],"first":[167],"time,":[168,260],"enables":[169],"us":[170],"adaptively":[172],"remove":[173],"severe":[175],"numerical":[176],"stiffness":[177],"imposed":[178],"rapidly":[181],"(especially":[184],"late":[186],"times)":[187],"accurately":[189],"compute":[190],"far":[194],"longer":[195],"times":[196],"than":[197],"could":[198],"previously":[199],"be":[200,230],"accomplished.":[201],"Numerical":[202],"tests":[203],"demonstrate":[204],"stable,":[209],"efficient,":[210],"accurate.":[212],"perform":[214],"simulations":[216,286],"different":[218],"widths":[222,282],"and,":[223],"can":[229],"very":[231],"complex,":[232],"find":[234,252],"generally":[236],"consistent":[237],"predictions":[240],"theory":[243],"regarding":[244],"particular,":[250],"when":[254],"b(t)":[256],"increases":[257],"exponentially":[258],"undergoes":[264],"sometimes":[267],"dramatic":[268],"morphological":[269],"but":[271],"eventually":[272],"shrinks":[273],"as":[274,304],"circle.":[276],"When":[277],"b=b_c_k,":[278],"or":[279],"larger":[280],"are":[283],"used,":[284],"reveal":[287],"long":[290],"times,":[291],"exhibits":[294],"novel,":[295],"strikingly":[296],"thin":[297],"k-fold":[298],"morphologies":[299],"do":[301],"not":[302,321],"vanish":[303],"shrinks,":[307],"suggesting":[308],"exists":[310],"mode":[311],"selection":[312],"regime":[316],"though":[317],"evolution":[319],"self-similar.":[322]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}