{"id":"https://openalex.org/W2026825964","doi":"https://doi.org/10.1145/1531326.1531344","title":"Energy-preserving integrators for fluid animation","display_name":"Energy-preserving integrators for fluid animation","publication_year":2009,"publication_date":"2009-07-27","ids":{"openalex":"https://openalex.org/W2026825964","doi":"https://doi.org/10.1145/1531326.1531344","mag":"2026825964"},"language":"en","primary_location":{"id":"doi:10.1145/1531326.1531344","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1531326.1531344","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","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/A5018235846","display_name":"Patrick Mullen","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick Mullen","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067419448","display_name":"Keenan Crane","orcid":"https://orcid.org/0000-0003-2772-7034"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Keenan Crane","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101533825","display_name":"Dmitry Pavlov","orcid":"https://orcid.org/0000-0002-9625-8027"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dmitry Pavlov","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042762771","display_name":"Yiying Tong","orcid":"https://orcid.org/0000-0002-7929-4333"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yiying Tong","raw_affiliation_strings":["MSU"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MSU","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022153785","display_name":"Mathieu Desbrun","orcid":"https://orcid.org/0000-0003-3424-6079"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mathieu Desbrun","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.3212,"has_fulltext":false,"cited_by_count":127,"citation_normalized_percentile":{"value":0.99632353,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"28","issue":"3","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9783999919891357,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9757000207901001,"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/inviscid-flow","display_name":"Inviscid flow","score":0.7116859555244446},{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.7110671997070312},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.671998143196106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6326361894607544},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5765897035598755},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.5596104264259338},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.49565231800079346},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.4422307014465332},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33915573358535767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30422210693359375},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2581908106803894},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.2163044810295105},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13939982652664185}],"concepts":[{"id":"https://openalex.org/C86252789","wikidata":"https://www.wikidata.org/wiki/Q2247765","display_name":"Inviscid flow","level":2,"score":0.7116859555244446},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.7110671997070312},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.671998143196106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6326361894607544},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5765897035598755},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.5596104264259338},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.49565231800079346},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.4422307014465332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33915573358535767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30422210693359375},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2581908106803894},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.2163044810295105},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13939982652664185},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1531326.1531344","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1531326.1531344","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:15821","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20090911-153604126","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G3182511187","display_name":null,"funder_award_id":"DE-FG02-04ER25657","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3557280242","display_name":null,"funder_award_id":"CCF-0811373/0811313DMS-0453145CMMI-0757106/0757123","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G412419981","display_name":null,"funder_award_id":"CCF-0811373/0811313DMS-0453145CMMI-0757106/0757123","funder_id":"https://openalex.org/F4320337391","funder_display_name":"Division of Civil, Mechanical and Manufacturing Innovation"},{"id":"https://openalex.org/G8003303817","display_name":null,"funder_award_id":"CCF-0811373/0811313DMS-0453145CMMI-0757106/0757123","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1956733578","https://openalex.org/W1966158133","https://openalex.org/W1977150043","https://openalex.org/W1981382127","https://openalex.org/W1985318753","https://openalex.org/W1988243598","https://openalex.org/W1993460192","https://openalex.org/W2005780385","https://openalex.org/W2018451527","https://openalex.org/W2022740560","https://openalex.org/W2031569927","https://openalex.org/W2032147135","https://openalex.org/W2042307687","https://openalex.org/W2052547843","https://openalex.org/W2071998665","https://openalex.org/W2078133941","https://openalex.org/W2088305381","https://openalex.org/W2088536902","https://openalex.org/W2096320147","https://openalex.org/W2099945117","https://openalex.org/W2108759333","https://openalex.org/W2126195192","https://openalex.org/W2141094169","https://openalex.org/W2141839129","https://openalex.org/W2141870784","https://openalex.org/W2161433140","https://openalex.org/W2162167019","https://openalex.org/W2167154018","https://openalex.org/W2237109911","https://openalex.org/W2295821368","https://openalex.org/W3141401227","https://openalex.org/W4211044098","https://openalex.org/W4245192669","https://openalex.org/W4250196415","https://openalex.org/W4256721759","https://openalex.org/W6674514985"],"related_works":["https://openalex.org/W1486213812","https://openalex.org/W2963995572","https://openalex.org/W2804509140","https://openalex.org/W1644877668","https://openalex.org/W1602020813","https://openalex.org/W3186153824","https://openalex.org/W4324319056","https://openalex.org/W2415733166","https://openalex.org/W3011178584","https://openalex.org/W2118166611"],"abstract_inverted_index":{"Numerical":[0],"viscosity":[1,67],"has":[2],"long":[3,105],"been":[4],"a":[5,37,92],"problem":[6],"in":[7,36,91,108],"fluid":[8,76],"animation.":[9],"Existing":[10],"methods":[11],"suffer":[12],"from":[13],"intrinsic":[14],"artificial":[15],"dissipation":[16],"and":[17,50,84,89,98],"often":[18],"apply":[19],"complicated":[20],"computational":[21],"mechanisms":[22],"to":[23,80,130],"combat":[24],"such":[25],"effects.":[26],"Consequently,":[27],"dissipative":[28],"behavior":[29],"cannot":[30],"be":[31,117],"controlled":[32],"or":[33],"modeled":[34],"explicitly":[35],"manner":[38,94],"independent":[39],"of":[40,47,71,75,111,122],"time":[41,106],"step":[42],"size,":[43],"complicating":[44],"the":[45,73,99,109,123],"use":[46],"coarse":[48],"previews":[49],"adaptive-time":[51],"stepping":[52],"methods.":[53],"This":[54],"paper":[55],"proposes":[56],"simple,":[57],"unconditionally":[58],"stable,":[59],"fully":[60],"Eulerian":[61],"integration":[62],"schemes":[63],"with":[64],"no":[65],"numerical":[66],"that":[68],"are":[69,86],"capable":[70],"maintaining":[72],"liveliness":[74],"motion":[77],"without":[78],"recourse":[79],"corrective":[81],"devices.":[82],"Pressure":[83],"fluxes":[85],"solved":[87],"efficiently":[88],"simultaneously":[90],"time-reversible":[93],"on":[95],"simplicial":[96,131],"grids,":[97],"energy":[100],"is":[101],"preserved":[102],"exactly":[103],"over":[104],"scales":[107],"case":[110],"inviscid":[112],"fluids.":[113],"These":[114],"integrators":[115],"can":[116],"viewed":[118],"as":[119],"an":[120],"extension":[121],"classical":[124],"energy-preserving":[125],"Harlow-Welch":[126],"/":[127],"Crank-Nicolson":[128],"scheme":[129],"grids.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}