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Type of Document	Master's Thesis
Author	Elcott, Sharif Mohamed
URN	etd-05272005-135652
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-05272005-135652
Title	Discrete, circulation-preserving, and stable simplicial fluids
Degree	Master of Science
Option	Computer Science
Advisory Committee	Advisor Name Title Peter Schroder Committee Chair
Keywords	Discrete Exterior Calculus Computational Algorithms Circulation Preservation Fluid Dynamics
Date of Defense	2005-05-27
Availability	unrestricted
Abstract 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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    DiscreteFluids.pdf 25.00 Mb 01:55:43 00:59:30 00:52:04 00:26:02 00:02:13