{"id":"https://openalex.org/W4283389067","doi":"https://doi.org/10.1137/21m141573x","title":"A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography","display_name":"A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4283389067","doi":"https://doi.org/10.1137/21m141573x"},"language":"en","primary_location":{"id":"doi:10.1137/21m141573x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m141573x","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/A5091293976","display_name":"Alexander Kurganov","orcid":"https://orcid.org/0000-0003-0231-986X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander Kurganov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009899507","display_name":"Yongle Liu","orcid":"https://orcid.org/0000-0003-0196-5050"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongle Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077357327","display_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1\u2013Medvid\u2019ov\u00e1","orcid":"https://orcid.org/0000-0002-4351-0161"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091293976"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3004,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75126113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"3","first_page":"A1655","last_page":"A1680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9988999962806702,"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":0.9988999962806702,"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9943000078201294,"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/mathematics","display_name":"Mathematics","score":0.8281213045120239},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6126098036766052},{"id":"https://openalex.org/keywords/froude-number","display_name":"Froude number","score":0.6110814809799194},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"Shallow water equations","score":0.5896459817886353},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.5196439027786255},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4971061050891876},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.4342307448387146},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.4205612540245056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41997456550598145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27623099088668823},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.23626714944839478},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07412642240524292}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8281213045120239},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6126098036766052},{"id":"https://openalex.org/C206835866","wikidata":"https://www.wikidata.org/wiki/Q273090","display_name":"Froude number","level":3,"score":0.6110814809799194},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.5896459817886353},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.5196439027786255},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4971061050891876},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.4342307448387146},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.4205612540245056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41997456550598145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27623099088668823},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.23626714944839478},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07412642240524292},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m141573x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m141573x","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":[{"display_name":"Clean water and sanitation","score":0.5799999833106995,"id":"https://metadata.un.org/sdg/6"}],"awards":[{"id":"https://openalex.org/G2124539424","display_name":null,"funder_award_id":"2019B030301001","funder_id":"https://openalex.org/F4320331067","funder_display_name":"Guangdong Provincial Key Laboratory Of Computational Science And Material Design"},{"id":"https://openalex.org/G225470762","display_name":null,"funder_award_id":"1201101343","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G25894984","display_name":null,"funder_award_id":"12171226","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3826898099","display_name":null,"funder_award_id":"11771201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322907","display_name":"Gutenberg Forschungskolleg","ror":"https://ror.org/023b0x485"},{"id":"https://openalex.org/F4320331067","display_name":"Guangdong Provincial Key Laboratory Of Computational Science And Material Design","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W205356147","https://openalex.org/W570977054","https://openalex.org/W1974309420","https://openalex.org/W1975706278","https://openalex.org/W1976724982","https://openalex.org/W2001032670","https://openalex.org/W2008076987","https://openalex.org/W2013753235","https://openalex.org/W2014836614","https://openalex.org/W2024240547","https://openalex.org/W2027557220","https://openalex.org/W2038747175","https://openalex.org/W2042336927","https://openalex.org/W2043057066","https://openalex.org/W2043134007","https://openalex.org/W2051165327","https://openalex.org/W2054420328","https://openalex.org/W2059466402","https://openalex.org/W2064480181","https://openalex.org/W2099564374","https://openalex.org/W2112548197","https://openalex.org/W2137755499","https://openalex.org/W2139737621","https://openalex.org/W2156669471","https://openalex.org/W2157862867","https://openalex.org/W2160514662","https://openalex.org/W2336994952","https://openalex.org/W2464136807","https://openalex.org/W2542590172","https://openalex.org/W2582103697","https://openalex.org/W2610658662","https://openalex.org/W2618073375","https://openalex.org/W2774510271","https://openalex.org/W2782116534","https://openalex.org/W2799904623","https://openalex.org/W2893933959","https://openalex.org/W2935711959","https://openalex.org/W2980402386","https://openalex.org/W3100306894","https://openalex.org/W4232473186","https://openalex.org/W4235094606","https://openalex.org/W4307237617"],"related_works":["https://openalex.org/W2743595507","https://openalex.org/W2093732976","https://openalex.org/W2384486693","https://openalex.org/W2432471543","https://openalex.org/W2366258330","https://openalex.org/W3192725306","https://openalex.org/W2105297067","https://openalex.org/W2005042969","https://openalex.org/W4284962501","https://openalex.org/W2531835128"],"abstract_inverted_index":{"We":[0,12,82,119,188],"consider":[1],"the":[2,15,23,85,93,99,104,121,124,142,146,150,155,159,165,169,190,195,211],"two-dimensional":[3],"rotating":[4],"shallow":[5],"water":[6],"equations":[7,87],"with":[8],"nonflat":[9],"bottom":[10],"topography.":[11],"focus":[13],"on":[14],"case":[16],"of":[17,61,68,90,92,145,158,168,194,202],"low":[18,62],"Froude":[19,63],"number,":[20],"in":[21,79,88,107],"which":[22,47,178,205],"system":[24,147],"is":[25,40,48,77,161,179],"stiff":[26,125,151,156],"and":[27,35,55,65,96,110,126,129,198,219],"conventional":[28],"explicit":[29,137],"numerical":[30,203],"methods":[31],"are":[32],"extremely":[33],"inefficient":[34],"often":[36],"impractical.":[37],"Our":[38],"goal":[39,76],"to":[41,103,141,172],"design":[42],"a":[43,58,174,182,200],"finite":[44],"volume":[45],"scheme,":[46],"both":[49],"asymptotic":[50,191,213],"preserving":[51,70,192,214],"(uniformly":[52],"asymptotically":[53],"consistent":[54],"stable":[56],"for":[57],"broad":[59],"range":[60],"numbers)":[64],"well-balanced":[66],"(capable":[67],"exactly":[69],"geophysically":[71],"relevant":[72],"steady-state":[73],"solutions).":[74],"The":[75],"achieved":[78],"two":[80],"steps.":[81],"first":[83],"rewrite":[84],"studied":[86],"terms":[89],"perturbations":[91],"steady":[94],"state":[95],"then":[97,130],"apply":[98,135],"flux":[100,122,160],"splitting":[101],"similar":[102],"one":[105],"used":[106],"[Liu,":[108,217],"Chertok,":[109,218],"Kurganov":[111,220],"J.":[112,221],"Comput.":[113,222],"Phys.,":[114,223],"391":[115,224],"(2019),":[116,225],"pp.":[117,226],"259-279].":[118,227],"split":[120],"into":[123],"nonstiff":[127,143],"parts":[128],"use":[131],"an":[132,136],"implicit-explicit":[133],"approach:":[134],"second-order":[138,184],"central-upwind":[139],"scheme":[140,197,209,215],"part":[144,152,157],"while":[148],"treating":[149],"implicitly.":[153],"As":[154],"linear,":[162],"we":[163],"reduce":[164],"implicit":[166],"stage":[167],"proposed":[170],"method":[171],"solving":[173],"Poisson-type":[175],"elliptic":[176],"equation,":[177],"discretized":[180],"using":[181],"standard":[183],"central":[185],"difference":[186],"scheme.":[187],"prove":[189],"property":[193],"developed":[196],"conduct":[199],"series":[201],"experiments,":[204],"demonstrate":[206],"that":[207],"our":[208],"outperforms":[210],"non-well-balanced":[212],"from":[216]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}