[ugrads] AMS President James Glimm to Speak at IIT on Friday, April 4
cronin at iit.edu
Fri Mar 28 15:15:29 CDT 2008
AMS President James Glimm to Speak at IIT on Friday, April 4
Dr. James Glimm will speak on "Macro/Micro Perspectives for Turbulent
Mixing: Large Scale and Atomic Scale Mixing Properties" on Friday, April 4,
12:45 p.m., Wishnick Hall Auditorium. Glimm is president of the American
Mathematical Society, a member of the National Academy of Sciences, 2002
winner of the National Medal of Science, and recipient of many other prizes
and awards. He is Chair and Distinguished Professor of Applied Mathematics
and Statistics at State University of New York at Stony Brook. Please RSVP
to cronin at iit.edu or 312-567-3132.
To learn more about Dr. Glimm, please visit
Numerical approximation of fluid equations are reviewed. We identify
numerical mass diffusion as a characteristic problem in most simulation
codes. This fact is illustrated by an analysis of fluid mixing flows. A main
problem for such flows is to sort out the distinct effects
of small and large scale mixing.
We study both large scale and atomic scale mixing properties for
classical hydrodynamic instabilities and mixing flows. The instability is
driven by acceleration directed across a density discontinuity in the fluid.
Assuming small scale initial perturbations of the interface, a highly
complex mixing zone develops when acceleration is applied to the fluids.
This simple sounding mixing flow has been notoriously difficult to predict.
Standard simulations may give results differing from experiments by factors
of two or more. We ascribe these differences to numerical
artifacts in the simulations, specifically numerical mass diffusion.
A number of additional startling conclusions have recently emerged. For a
flow accelerated by multiple shock waves, we observe an interface between
the two fluids proportional to Delta x^-1, that is occupying a constant
fraction of the available mesh degrees of freedom. This result suggests (a)
nonconvergence for the mathematical problem or (b) nonuniqueness of the
limit if it exists, or (c) limiting solutions only in the very weak form of
a space time dependent probability distribution.
The cure for this pathology is a regularized solution, in other
words inclusion of all physical regularizing effects, such as viscosity and
physical mass diffusion. Once this is done, the solution appears to depend
on the ratio of the coefficients in these terms, such as the
Schmidt number, or if the solution is under resolved, on a numerical and
code dependent Schmidt number.
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