The first two dayw: basic techniques
In the first day the accent will be on basic ideas, in particular
the method of asymptotic expansion and how this can be applied to
problems with highly oscillatory characteristics. The aim is to
develop effective (upscaled) equations where the oscillations are
averaged out, but which are still able to describe the averaged
behavior of the system.
The techniques introduced in the first days are further employed
in the second day to deal with complex (perforated) domains, such
as porous media. Specifically, these idea will be employed for the
derivation of the Darcy law and for constructing upscaled models
for diffusion, convection, reaction and adsorption in porous
media.
Recommended reading:
Homogenization and porous media (Chapters 1 and 6). Edited by
Ulrich Hornung. Interdisciplinary Applied Mathematics, 6.
Springer-Verlag, New York, 1997.