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Discrete, circulation-preserving, and stable simplicial fluids


Elcott, Sharif Mohamed (2005) Discrete, circulation-preserving, and stable simplicial fluids. Master's thesis, California Institute of Technology.


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 has 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 thesis we describe 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; (4) it preserves discrete circulation avoiding numerical diffusion of vorticity; and (5) its implementation is straightforward.

Item Type:Thesis (Master's thesis)
Subject Keywords:Circulation Preservation; Computational Algorithms; Discrete Exterior Calculus; Fluid Dynamics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Schroeder, Peter
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 May 2005
Record Number:CaltechETD:etd-05272005-135652
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2152
Deposited By: Imported from ETD-db
Deposited On:01 Jun 2005
Last Modified:26 Dec 2012 02:47

Thesis Files

PDF (DiscreteFluids.pdf) - Final Version
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