A substantial part of our research is concerned with the simulation of multiphase flows in porous media. In particular we develop a dedicated software, the code ComPASS. This activity is the object of fruitful collaborations, in particular with BRGM. We display a few examples of geothermal simulation in faulted reservoirs.
We are particularly interested in the development and analysis of Finite Volume Methods for flows in porous media, and complex viscous flows. For instance, we pay specific attention to the Discrete Duality Finite Volume approach.
We have developped original numerical strategies, based on staggered Finite Volume discretisations, for the Euler equations, and more generally for the simulation of mixture flows.
We have derived a new hierarchy of models describing self-organization phenomena in populations driven by pursuit-evasion dynamics. The models range from ODEs system (individual-based modeling) to conservation laws (hydrodynamic-like modeling), including kinetic equations having the flavor of statistical physics. This is a joint work with T. Goudon, B. Nkonga, M. Rascle and M. Ribot.
Naively, the dynamic can be though of like a “cops and robbers game”, but the terminology is used in mathematics and in computer sciences to a specific and different field (having some connection with graph theory).
It is worth looking at the movies that correspond to 2D simulations with either Neumann boundary conditions or periodic boundary conditions. Despite the simplicity of the model, interesting phenomena can be observed.