Numerical Simulation of Vortex Filament Flow

Abstract:

The Vortex Filament Flow has many interesting geometric and algebraic properties. In order to understand how the flow evolves curves, it is necessary to perform tedious calculations or execute a thought experiment, using the geometric properties of the flow to obtain a mental picture of the evolution. This project had as its primary focus the construction of a computer program that would perform the tedious calculations involved and generate a three dimensional movie of the flow over a specified time interval. A variety of input options and formats are available in order to provide the most flexible evolution program possible. This program is especially useful for simulating the evolution of more complex space curves, since their geometries are not necessarily easy to visualize.

Faculty Advisors: Annalisa Calini and Tom Ivey