{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:47:41Z","timestamp":1769561261345,"version":"3.49.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2009,7,27]],"date-time":"2009-07-27T00:00:00Z","timestamp":1248652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-FG02-04ER25657"],"award-info":[{"award-number":["DE-FG02-04ER25657"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"],"award-info":[{"award-number":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"],"award-info":[{"award-number":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"],"award-info":[{"award-number":["CCF-0811373\/0811313DMS-0453145CMMI-0757106\/0757123"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2009,7,27]]},"abstract":"<jats:p>Numerical viscosity has long been a problem in fluid animation. Existing methods suffer from intrinsic artificial dissipation and often apply complicated computational mechanisms to combat such effects. Consequently, dissipative behavior cannot be controlled or modeled explicitly in a manner independent of time step size, complicating the use of coarse previews and adaptive-time stepping methods. This paper proposes simple, unconditionally stable, fully Eulerian integration schemes with no numerical viscosity that are capable of maintaining the liveliness of fluid motion without recourse to corrective devices. Pressure and fluxes are solved efficiently and simultaneously in a time-reversible manner on simplicial grids, and the energy is preserved exactly over long time scales in the case of inviscid fluids. These integrators can be viewed as an extension of the classical energy-preserving Harlow-Welch \/ Crank-Nicolson scheme to simplicial grids.<\/jats:p>","DOI":"10.1145\/1531326.1531344","type":"journal-article","created":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T12:43:55Z","timestamp":1248785035000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":94,"title":["Energy-preserving integrators for fluid animation"],"prefix":"10.1145","volume":"28","author":[{"given":"Patrick","family":"Mullen","sequence":"first","affiliation":[{"name":"Caltech"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keenan","family":"Crane","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Pavlov","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiying","family":"Tong","sequence":"additional","affiliation":[{"name":"MSU"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mathieu","family":"Desbrun","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2009,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276439"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(86)90211-1"},{"key":"e_1_2_2_4_1","volume-title":"Symposium on Computer Animation, 219--228","author":"Chentanez N.","unstructured":"Chentanez , N. , Feldman , B. E. , Labelle , F. , O'Brien , J. F. , and Shewchuk , J . 2007. Liquid simulation on latticebased tetrahedral meshes . In Symposium on Computer Animation, 219--228 . Chentanez, N., Feldman, B. E., Labelle, F., O'Brien, J. F., and Shewchuk, J. 2007. Liquid simulation on latticebased tetrahedral meshes. In Symposium on Computer Animation, 219--228."},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Chorin A. and Marsden J. 1979. A Mathematical Introduction to Fluid Mechanics 3rd edition ed. Springer-Verlag.  Chorin A. and Marsden J. 1979. A Mathematical Introduction to Fluid Mechanics 3rd edition ed. Springer-Verlag.","DOI":"10.1007\/978-1-4684-0082-3"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.06.020"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1189762.1189766"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383260"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882336"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073281"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258838"},{"key":"e_1_2_2_12_1","unstructured":"Gresho P. M. and Sani R. L. 2000. Incompressible Flow and the Finite Element Method. J. Wiley &amp; Sons.  Gresho P. M. and Sani R. L. 2000. Incompressible Flow and the Finite Element Method . J. Wiley &amp; Sons."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1761178"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.3"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015745"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.031"},{"key":"e_1_2_2_17_1","volume-title":"Symposium on Computer Animation, 9--18","author":"Molemaker J.","year":"2008","unstructured":"Molemaker , J. , Cohen , J. M. , Patel , S. , and Yong Noh , J. 2008 . Low viscosity flow simulations for animation . In Symposium on Computer Animation, 9--18 . Molemaker, J., Cohen, J. M., Patel, S., and Yong Noh, J. 2008. Low viscosity flow simulations for animation. In Symposium on Computer Animation, 9--18."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6424"},{"key":"e_1_2_2_20_1","volume-title":"Symposium on Computer Animation, 1--8.","author":"Schechter H.","unstructured":"Schechter , H. , and Bridson , R . 2008. Evolving sub-grid turbulence for smoke animation . In Symposium on Computer Animation, 1--8. Schechter, H., and Bridson, R. 2008. Evolving sub-grid turbulence for smoke animation. In Symposium on Computer Animation, 1--8."},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073282"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-007-9166-4"},{"key":"e_1_2_2_23_1","unstructured":"Shi L. and Yu Y. 2002. Visual smoke simulation with adaptive octree refinement. Computer Graphics and Imaging.  Shi L. and Yu Y. 2002. Visual smoke simulation with adaptive octree refinement. Computer Graphics and Imaging ."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90042-6"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311548"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.868164"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1185657.1185669"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6973"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1186822.1073298"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531344","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1531326.1531344","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:30:23Z","timestamp":1750253423000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1531326.1531344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,27]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,7,27]]}},"alternative-id":["10.1145\/1531326.1531344"],"URL":"https:\/\/doi.org\/10.1145\/1531326.1531344","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,27]]},"assertion":[{"value":"2009-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}