vort_treecode is a program that computes the evolution of a three-dimensional vortex sheet using an adaptive treecode to evaluate the velocity field.

The program was developed for my Ph.D. dissertation, under the supervision of Robert Krasny in the Mathematics Department at The University of Michigan.

My Ph.D. research was supported by a grant from the National Science Foundation.

Access to the sourcecode

A cleaned up version the sourcecode is available under the GNU General Public License.

Version 1.0 is available in a tar-file here : vort_treecode_1_0.tar.

Included in the tar-file is the following README file.


double spaced format: thesis2.pdf

single spaced format: thesis.pdf


The code is described in the following two references. If you publish an article that relies on the code, please cite them.

Keith Lindsay, 'A Three-Dimensional Cartesian Tree-Code and Applications to Vortex Sheet Roll-up', Ph.D. Dissertation, The University of Michigan, 1997.

K. Lindsay and R. Krasny, 'A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow', Journal of Computational Physics, Vol. 172, No. 2, 2001, pp. 879-907.

Selected Graphics

Here are a few images of colliding vortex sheets from a simulation that is described in both of the reference above.

cut-away of colliding sheets @ time 2.0

cut-away of colliding sheets @ time 3.0

cut-away of colliding sheets @ time 4.0

cut-away of colliding sheets @ time 4.5

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Last Modified : Friday, 19-May-2006 20:59:39 MDT