Article

Discrete, vorticity-preserving, and stable simplicial fluids

Authors:

Peter Schröder,

Mathieu DesbrunAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Courses

Pages 9 - es

https://doi.org/10.1145/1198555.1198668

Published: 31 July 2005 Publication History

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.

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Cited By

Huang ZGong GHan L(2015)Physically-based smoke simulation for computer graphicsMultimedia Tools and Applications10.1007/s11042-014-1992-474:18(7569-7594)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s11042-014-1992-4
Desbrun MKanso ETong YFinnegan JShreiner D(2006)Discrete differential forms for computational modelingACM SIGGRAPH 2006 Courses10.1145/1185657.1185665(39-54)Online publication date: 30-Jul-2006
https://dl.acm.org/doi/10.1145/1185657.1185665
Klingner BFeldman BChentanez NO'Brien J(2006)Fluid animation with dynamic meshesACM Transactions on Graphics10.1145/1141911.114196125:3(820-825)Online publication date: 1-Jul-2006
https://dl.acm.org/doi/10.1145/1141911.1141961
Show More Cited By

Discrete, vorticity-preserving, and stable simplicial fluids
1. Computing methodologies
  1. Computer graphics

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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Courses

July 2005

7157 pages

ISBN:9781450378338

DOI:10.1145/1198555

Editor:
John Fujii
Hewlett-Packard Company

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 31 July 2005

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Cited By

Huang ZGong GHan L(2015)Physically-based smoke simulation for computer graphicsMultimedia Tools and Applications10.1007/s11042-014-1992-474:18(7569-7594)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s11042-014-1992-4
Desbrun MKanso ETong YFinnegan JShreiner D(2006)Discrete differential forms for computational modelingACM SIGGRAPH 2006 Courses10.1145/1185657.1185665(39-54)Online publication date: 30-Jul-2006
https://dl.acm.org/doi/10.1145/1185657.1185665
Klingner BFeldman BChentanez NO'Brien J(2006)Fluid animation with dynamic meshesACM Transactions on Graphics10.1145/1141911.114196125:3(820-825)Online publication date: 1-Jul-2006
https://dl.acm.org/doi/10.1145/1141911.1141961
Feldman BO'Brien JKlingner B(2005)Animating gases with hybrid meshesACM Transactions on Graphics10.1145/1073204.107328124:3(904-909)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1145/1073204.1073281

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