Colloquia

CAM DISTINGUISHED LECTURER SERIES

“Computational Fluid Dynamics”

James Glimm
Department of Applied Mathematics and Statistics
Stony Brook University
President, American Mathematical Society

Monday - September 17, 2007
4:00PM in 127 Hayes-Healy Center
*TEA AT 3:30PM in the Math Lounge - 257 Hurley*

Abstract:

Many of the equations of continuum physics are described by conservation laws, and in an approximation, the time dependence in these laws gives rise to hyperbolic equations. Theory is mainly limited to one spatial dimension, while numerical experience, accumulated over many decades, applies to many fully 3D flows. Surprisingly, the major numerical difficulties are those associated with the linear (contact) waves within these systems, such as thermal or shear layers.

We explore flows in which these contact waves define chaotic features. One sign of chaos is a fractal property for the evolving contact interface, in cases where the underlying flow is turbulent. We suggest that the computation, at a hyperbolic level, is indeterminate, and that scale breaking, non hyperbolic physics (transport, such as viscosity or mass diffusion) is needed to yield a well posed problem.