Seminar Details:

LANS Informal Seminar
"Computing Vortex Sheet Motion"

DATE: May 11, 2011

TIME: 15:00:00 - 16:00:00
SPEAKER: Robert Krasny, University of Michigan
LOCATION: Building 240, Conference Center 1404-1405, Argonne National Laboratory

Description:
Vortex sheets are used in fluid dynamics to model thin shear layers in slightly viscous flow. Examples include mixing layers subject to Kelvin-Helmholtz instability and airplane trailing wakes. One of the earliest simulations in computational fluid dynamics used the point vortex method to compute vortex sheet motion. The results seemed to confirm Prandtl's idea that vortex sheets roll up smoothly into concentrated spirals, but later simulations with higher resolution encountered difficulty due to ill-posedness and singularity formation. I'll describe the fundamental contributions on this topic by Louis Rosenhead, Garrett Birkhoff, and Derek Moore, and then discuss more recent regularized simulations past the critical time. The results support a conjecture by Dale Pullin on self-similarity, but chaos intervenes unexpectedly. Then I'll describe a new panel method for vortex sheet motion in 3D flow which uses a Cartesian treecode for efficiency. An application to vortex rings will be presented. Finally I'll indicate briefly how the treecode is being used in other problems involving long-range particle interactions.


 

Please send questions or suggestions to Debojyoti Ghosh: ghosh at mcs dot anl dot gov.