Lecture 2 Homogenization in Porous Media

The goal of this lecture is to show that homogenization is a very efficient tool in the modeling of complex phenomena in heterogeneous media. In the first lecture we considered a model problem of diffusion for which the homogenized operator was of the same type (still a diffusion equation). In this context, homogenization is really a matter of defining and computing effective diffusion tensors. On the contrary, this second lecture will focus on models which have different homogenized limits (in the sense that the partial differential equations are of a different mathematical nature). For example, we shall see that the Stokes equations for a viscous fluid in a porous medium yield the Darcy’s law as an homogenized model. Therefore, in this context, homogenization is a modeling tool which can justify new models arising as homogenized limits of complex microscopic equations.