{"id":"https://openalex.org/W1604788505","doi":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","title":"A Fast and Compact Solver for the Shallow Water Equations","display_name":"A Fast and Compact Solver for the Shallow Water Equations","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1604788505","doi":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","mag":"1604788505"},"language":"en","primary_location":{"id":"doi:10.2312/pe/vriphys/vriphys07/051-057","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020595766","display_name":"Richard Lee","orcid":"https://orcid.org/0000-0003-4687-1381"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lee, Richard","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063212917","display_name":"Carol O\u2019Sullivan","orcid":"https://orcid.org/0000-0003-3772-4961"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"O'Sullivan, Carol","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020595766"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9955000281333923,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9905999898910522,"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/shallow-water-equations","display_name":"Shallow water equations","score":0.7637131214141846},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7112162709236145},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6587579846382141},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6489629149436951},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.6330618262290955},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4968264400959015},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48404234647750854},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.476154088973999},{"id":"https://openalex.org/keywords/waves-and-shallow-water","display_name":"Waves and shallow water","score":0.4400154650211334},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4289041757583618},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4284972846508026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40199705958366394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40122514963150024},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34247857332229614},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.23728123307228088},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2338484823703766},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1525866687297821},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14666694402694702}],"concepts":[{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.7637131214141846},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7112162709236145},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6587579846382141},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6489629149436951},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.6330618262290955},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4968264400959015},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48404234647750854},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.476154088973999},{"id":"https://openalex.org/C186348155","wikidata":"https://www.wikidata.org/wiki/Q7975538","display_name":"Waves and shallow water","level":2,"score":0.4400154650211334},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4289041757583618},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4284972846508026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40199705958366394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40122514963150024},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34247857332229614},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.23728123307228088},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2338484823703766},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1525866687297821},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14666694402694702},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/pe/vriphys/vriphys07/051-057","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.2312/pe/vriphys/vriphys07/051-057","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vriphys/vriphys07/051-057","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/6","score":0.7599999904632568,"display_name":"Clean water and sanitation"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965214225","https://openalex.org/W1975943852","https://openalex.org/W1981382127","https://openalex.org/W1995828250","https://openalex.org/W2035545087","https://openalex.org/W2059753342","https://openalex.org/W2073625970","https://openalex.org/W2092767817","https://openalex.org/W2098588961","https://openalex.org/W2104805498","https://openalex.org/W2126370801","https://openalex.org/W2142688536","https://openalex.org/W2161352018","https://openalex.org/W2237109911","https://openalex.org/W2295821368","https://openalex.org/W2579989840"],"related_works":["https://openalex.org/W2098588961","https://openalex.org/W2293709945","https://openalex.org/W2187602572","https://openalex.org/W2161352018","https://openalex.org/W2145868598","https://openalex.org/W2126370801","https://openalex.org/W300273075","https://openalex.org/W2770565528","https://openalex.org/W2201489423","https://openalex.org/W2118617078","https://openalex.org/W2752525416","https://openalex.org/W1773643800","https://openalex.org/W2294502813","https://openalex.org/W2087275991","https://openalex.org/W2028451650","https://openalex.org/W2116267936","https://openalex.org/W2075250962","https://openalex.org/W2015159084","https://openalex.org/W1974916751","https://openalex.org/W2950766779"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,23,27,49],"fast":[4,71],"and":[5,17,26,56,70],"simple":[6],"method":[7],"for":[8,59,73],"solving":[9,48],"the":[10,41],"shallow":[11],"water":[12,15],"equations.":[13],"The":[14],"velocity":[16],"height":[18],"variables":[19],"are":[20],"collocated":[21],"on":[22],"uniform":[24],"grid":[25],"novel,":[28],"unified":[29],"scheme":[30],"is":[31,67],"used":[32],"to":[33,46],"advect":[34],"all":[35],"quantities":[36],"together.":[37],"Furthermore,":[38],"we":[39,62],"treat":[40],"fluid":[42],"as":[43],"weakly":[44],"compressible":[45],"avoid":[47],"pressure":[50],"Poisson":[51],"equation.":[52],"We":[53],"sacrifice":[54],"accuracy":[55],"unconditional":[57],"stability":[58],"speed,":[60],"but":[61],"show":[63],"that":[64],"our":[65],"algorithm":[66],"sufficiently":[68],"stable":[69],"enough":[72],"real-time":[74],"applications.":[75]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
