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In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently, often introduce a visually disturbing numerical diffusion of\n            <jats:italic>vorticity<\/jats:italic>\n            . Just as important visually is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally delicate. In this article, we propose a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, that is, the\n            <jats:italic>conservation of circulation<\/jats:italic>\n            along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: Arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; the computations involved in the update procedure are efficient due to discrete operators with small support; and it preserves\n            <jats:italic>discrete circulation<\/jats:italic>\n            , avoiding numerical diffusion of vorticity.\n          <\/jats:p>","DOI":"10.1145\/1189762.1189766","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"4","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":145,"title":["Stable, circulation-preserving, simplicial fluids"],"prefix":"10.1145","volume":"26","author":[{"given":"Sharif","family":"Elcott","sequence":"first","affiliation":[{"name":"Caltech, Pasadena, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiying","family":"Tong","sequence":"additional","affiliation":[{"name":"Caltech, Pasadena, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eva","family":"Kanso","sequence":"additional","affiliation":[{"name":"USC, Los Angeles, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Caltech, Pasadena, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathieu","family":"Desbrun","sequence":"additional","affiliation":[{"name":"Caltech, Pasadena, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2007,1]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Eds","author":"Abraham R.","year":"1988","unstructured":"Abraham , R. , Marsden , J. , and Ratiu , T. , Eds . 1988 . 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