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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. https://resolver.caltech.edu/CaltechAUTHORS:20161011-165249647

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Abstract

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
http://dx.doi.org/10.1145/1198555.1198668DOIArticle
http://dl.acm.org/citation.cfm?doid=1198555.1198668PublisherArticle
ORCID:
AuthorORCID
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
DOI:10.1145/1198555.1198668
Record Number:CaltechAUTHORS:20161011-165249647
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161011-165249647
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=http://dx.doi.org/10.1145/1198555.1198668
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71006
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:12 Oct 2016 16:27
Last Modified:11 Nov 2021 04:38

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