Influence of the anisotropy

As we know the large majority of porous media that we can find in industry or in the nature present an anisotropy. It's why it is interesting to understand the influence of the anisotropy on the flow.

In order to take into account the anisotropy, we define the permeability as a tensor field in $m^2$:

 

First of all we study a case with K defined as a tensor but without anisotropy in $m^2$:

Then we can notice, that in the anisotropic K introduced, the permeability is more important in the horizontal direction than in the vertical or perpendicularly direction. Which means that we should have a more important velocity in the horizontal direction.

 

In the following study the gravity influence was neglected.