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HOLA: a High-Order Lie Advection of discrete differential forms, with applications in fluid dynamics

Citation

McKenzie, Alexander (2007) HOLA: a High-Order Lie Advection of discrete differential forms, with applications in fluid dynamics. Master's thesis, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05292007-100432

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.

Item Type:Thesis (Master's thesis)
Subject Keywords:Discrete differential forms; Lie derivative; Vorticity advection; WENO
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Desbrun, Mathieu
Thesis Committee:
  • Unknown, Unknown
Defense Date:25 May 2007
Author Email:am (AT) caltech.edu
Record Number:CaltechETD:etd-05292007-100432
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05292007-100432
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2246
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:30 May 2007
Last Modified:26 Dec 2012 02:48

Thesis Files

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[img] Video (AVI) (FluidInterface.avi) - Final Version
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[img] Video (AVI) (hola1.avi) - Final Version
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[img] Video (AVI) (Pseudospectral.avi) - Final Version
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