Multidomain simulation of flow in porous media

I will present during this seminar the main results of my PhD thesis
performed at Inria under the direction of Jean Roberts.

It is mainly concerned with the multidomain simulations
of flow in porous media. Three different themes are considered.
First, I present a domain decomposition method with non-matching meshes
using Robin type interface conditions, for the mixed finite
elements. Second, this method was implemented in parallel
using the parallel system OcamlP3l, written in Ocaml by
computer scientists. In OcamlP3l, the user develops and
debugs sequentially, and obtains the parallel code
with a mere recompilation. A realistic 3D simulation is
given to validate the procedure.
Finally, we present a new model for flow in a porous medium containing
large fractures that may have very large and/or very small permeabilities.
In this model, the fractures are treated as interfaces between subdomains.
Existence and uniqueness of the solution is proved and an error estimate is
obtained. Some numerical experiments confirm the theorical results.