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Type of Document	Master's Thesis
Author	McKenzie, Alexander
Author's Email Address	am@caltech.edu
URN	etd-05292007-100432
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-05292007-100432
Title	HOLA: a High-Order Lie Advection of discrete differential forms, with applications in fluid dynamics
Degree	Master of Science
Option	Computer Science
Advisory Committee	Advisor Name Title Mathieu Desbrun Committee Chair
Keywords	Discrete differential forms WENO Lie derivative Vorticity advection
Date of Defense	2007-05-25
Availability	unrestricted
Abstract The Lie derivative, and Exterior Calculus in general, is ubiquitous in the elegant geometric interpretation of many dynamical systems. We extend recent trends towards a Discrete Exterior Calculus by introducing a discrete framework for the Lie derivative defined on differential forms, including a WENO based numerical scheme for its implementation. The usefulness of this operator is demonstrated through the advection of scalar and vector valued fields (arbitrary discrete k-forms) in a desirable intrinsic and metric independent fashion. Examples include Lie advection of fluid flow vorticity, and we conclude with a significant discussion on the conservative Lie advection of fluid mass density for robust free surface flows in computer graphics.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Elcott.avi 439.88 Kb 00:02:02 00:01:02 00:00:54 00:00:27 00:00:02   FluidInterface.avi 29.30 Mb 02:15:38 01:09:45 01:01:02 00:30:31 00:02:36   hola1.avi 451.18 Kb 00:02:05 00:01:04 00:00:56 00:00:28 00:00:02   hola7.avi 1.21 Mb 00:05:35 00:02:52 00:02:31 00:01:15 00:00:06   HolaMS.pdf 835.76 Kb 00:03:52 00:01:59 00:01:44 00:00:52 00:00:04   Pseudospectral.avi 1.18 Mb 00:05:27 00:02:48 00:02:27 00:01:13 00:00:06