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Stable, circulation-preserving, simplicial fluids

Elcott, Sharif and Tong, Yiying and Kanso, Eva and Schröder, Peter and Desbrun, Mathieu (2007) Stable, circulation-preserving, simplicial fluids. ACM Transactions on Graphics (TOG), 26 (1). Art. No. 4. ISSN 0730-0301. doi:10.1145/1189762.1189766.

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Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid and deformable body simulation benefits greatly from the conservation of linear and angular momenta. 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 vorticity. 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 conservation of circulation 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 discrete circulation, avoiding numerical diffusion of vorticity.

Item Type:Article
Related URLs:
URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2007 ACM. Received August 2005; accepted October 2006. This work was partially supported by the NSF (DMS-0453145, CCF-0503786, CCF-0528101, ACI-0219979, CCR-0133983), the DOE (DE-FG02-04ER25657, W-7405-ENG-48/B341492), the Center for Integrative Multiscale Modeling and Simulation at Caltech, the Okawa Foundation, the Irvine Foundation, the Center for the Mathematics of Information, Autodesk, and Pixar Animation Studios.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-04ER25657
Department of Energy (DOE)W-7405-ENG-48/B341492
Center for Integrative Multiscale Modeling and Simulation, CaltechUNSPECIFIED
Okawa FoundationUNSPECIFIED
James Irvine FoundationUNSPECIFIED
Center for the Mathematics of Information, CaltechUNSPECIFIED
Pixar Animation StudiosUNSPECIFIED
Subject Keywords:Algorithm, Theory, Fluid animation, stable fluids, vorticity preservation, Lie advection
Issue or Number:1
Classification Code: I.3.6 [ Computer Graphics ]: Methodology and Techniques
Record Number:CaltechAUTHORS:20161013-130615464
Persistent URL:
Official Citation:Sharif Elcott, Yiying Tong, Eva Kanso, Peter Schröder, and Mathieu Desbrun. 2007. Stable, circulation-preserving, simplicial fluids. ACM Trans. Graph. 26, 1, Article 4 (January 2007). DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71057
Deposited On:13 Oct 2016 21:06
Last Modified:11 Nov 2021 04:39

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