{"id":"https://openalex.org/W2962820972","doi":"https://doi.org/10.1145/3309486.3339890","title":"Divergence-free and boundary-respecting velocity interpolation using stream functions","display_name":"Divergence-free and boundary-respecting velocity interpolation using stream functions","publication_year":2019,"publication_date":"2019-07-19","ids":{"openalex":"https://openalex.org/W2962820972","doi":"https://doi.org/10.1145/3309486.3339890","mag":"2962820972"},"language":"en","primary_location":{"id":"doi:10.1145/3309486.3339890","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3309486.3339890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 18th annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation","raw_type":"proceedings-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/A5047834276","display_name":"Jumyung Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jumyung Chang","raw_affiliation_strings":["University of Waterloo"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112368463","display_name":"Vin\u00edcius C. Azevedo","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Vinicius C. Azevedo","raw_affiliation_strings":["ETH Zurich"],"affiliations":[{"raw_affiliation_string":"ETH Zurich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046631319","display_name":"Christopher Batty","orcid":"https://orcid.org/0000-0003-3830-7772"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Christopher Batty","raw_affiliation_strings":["University of Waterloo"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047834276"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12872774,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9851999878883362,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9843999743461609,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.7687167525291443},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6517828702926636},{"id":"https://openalex.org/keywords/stream-function","display_name":"Stream function","score":0.6489524841308594},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.5909597277641296},{"id":"https://openalex.org/keywords/divergence-theorem","display_name":"Divergence theorem","score":0.5252037644386292},{"id":"https://openalex.org/keywords/particle-velocity","display_name":"Particle velocity","score":0.5208964347839355},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.519802451133728},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4682905077934265},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.46510323882102966},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4578711986541748},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4454461336135864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44189995527267456},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.327640175819397},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2745882272720337},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2688034176826477},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1681242287158966},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.16290658712387085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15524181723594666},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.1060681939125061}],"concepts":[{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.7687167525291443},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6517828702926636},{"id":"https://openalex.org/C18932819","wikidata":"https://www.wikidata.org/wiki/Q2029236","display_name":"Stream function","level":4,"score":0.6489524841308594},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.5909597277641296},{"id":"https://openalex.org/C16030659","wikidata":"https://www.wikidata.org/wiki/Q338886","display_name":"Divergence theorem","level":4,"score":0.5252037644386292},{"id":"https://openalex.org/C35515768","wikidata":"https://www.wikidata.org/wiki/Q336894","display_name":"Particle velocity","level":2,"score":0.5208964347839355},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.519802451133728},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4682905077934265},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.46510323882102966},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4578711986541748},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4454461336135864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44189995527267456},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.327640175819397},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2745882272720337},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2688034176826477},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1681242287158966},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.16290658712387085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15524181723594666},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.1060681939125061},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3309486.3339890","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3309486.3339890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 18th annual ACM SIGGRAPH/Eurographics Symposium on Computer Animation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1966158133","https://openalex.org/W1971960215","https://openalex.org/W2062242999","https://openalex.org/W2075599725","https://openalex.org/W2089344418","https://openalex.org/W2134066908","https://openalex.org/W2295821368","https://openalex.org/W3136918727","https://openalex.org/W4233546237"],"related_works":["https://openalex.org/W1600322409","https://openalex.org/W4318373019","https://openalex.org/W4297961796","https://openalex.org/W47835102","https://openalex.org/W2911915493","https://openalex.org/W4247715766","https://openalex.org/W1984175112","https://openalex.org/W4389457738","https://openalex.org/W2377878646","https://openalex.org/W2777055456"],"abstract_inverted_index":{"In":[0],"grid-based":[1],"fluid":[2,113,118],"simulation,":[3],"discrete":[4,22],"incompressibility":[5],"of":[6,80],"each":[7],"cell":[8,95],"is":[9],"enforced":[10],"by":[11,19,73],"the":[12,21,26,78],"pressure":[13],"projection.":[14],"However,":[15],"pointwise":[16],"velocities":[17],"constructed":[18],"interpolating":[20],"velocity":[23,50,57],"samples":[24],"from":[25],"staggered":[27],"grid":[28],"are":[29,68,110],"not":[30,121],"truly":[31],"divergence-free,":[32],"resulting":[33,66],"in":[34,59],"unphysical":[35],"local":[36],"volume":[37],"changes":[38],"that":[39,53,100],"manifests":[40],"as":[41],"particle":[42],"spreading":[43],"and":[44,115,117],"clustering.":[45],"We":[46],"present":[47],"a":[48,62,74,85],"new":[49],"interpolation":[51],"method":[52,91],"produces":[54],"analytically":[55],"divergence-free":[56,72,86],"fields":[58,67,99],"2D":[60],"using":[61],"stream":[63],"function.":[64],"The":[65],"guaranteed":[69],"to":[70,97],"be":[71],"simple":[75],"calculus":[76],"identity:":[77],"curl":[79],"any":[81],"vector":[82,87],"field":[83],"yields":[84],"field.":[88],"Furthermore,":[89],"our":[90],"works":[92],"on":[93],"cut":[94],"grids":[96],"produce":[98],"strictly":[101],"obey":[102],"solid":[103,124],"boundary":[104],"conditions.":[105],"Therefore,":[106],"no":[107],"artificial":[108],"gaps":[109],"created":[111],"between":[112],"particles":[114,119],"solids,":[116],"do":[120],"trespass":[122],"into":[123],"regions.":[125]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}