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.

Thesis Files