A Caltech Library Service

Discrete, Vorticity-Preserving, and Stable Simplicial Fluids

Elcott, Sharif and Tong, Yiying and Kanso, Eva and Schröder, Peter and Desbrun, Mathieu (2005) Discrete, Vorticity-Preserving, and Stable Simplicial Fluids. In: SIGGRAPH '05 ACM SIGGRAPH 2005 Courses. ACM , New York, NY, Art. No. 9.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


Visual accuracy, 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 or deformable body simulation have benefited greatly from conservation of linear and angular momenta. In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently, they often introduce a visually disturbing numerical diffusion of vorticity. Visually just as important is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally delicate. In this chapter, we propose a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, i.e., the conservation of circulation along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: (1) arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; (2) the computations are efficient due to discrete operators with small support; (3) the method is stable for arbitrarily large time steps; and (4) it preserves a discrete circulation avoiding numerical diffusion of vorticity. The underlying ideas are easy to incorporate in current approaches to fluid simulation and should thus prove valuable in many applications.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2005 ACM.
Subject Keywords:Fluid Dynamics, Discrete Exterior Calculus, Computational Algorithms, Circulation Preservation
Record Number:CaltechAUTHORS:20161011-165249647
Persistent URL:
Official Citation:Sharif Elcott, Yiying Tong, Eva Kanso, Peter Schröder, and Mathieu Desbrun. 2005. Discrete, vorticity-preserving, and stable simplicial fluids. In ACM SIGGRAPH 2005 Courses (SIGGRAPH '05), John Fujii (Ed.). ACM, New York, NY, USA, , Article 9 . DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71006
Deposited By: Kristin Buxton
Deposited On:12 Oct 2016 16:27
Last Modified:11 Nov 2021 04:38

Repository Staff Only: item control page