Benoît Desjardins, in charge of the scientific department of privately held company Modeling Measurements and Applications (MOMA), joins the FMJH (hosted by CMLA at ENS Cachan) on a part time basis. As a very active researcher (see resume), his experience with research in Industry will benefit to the FMJH (firstname.lastname@example.org).
Current research areas
The main current research domains of Benoit Desjardins involve mathematical analysis of complex multiphase flows for compressible or incompressible fluids, miscible or not, in laminar or turbulent regimes.
- Immiscible free surface fluid flows
The aim is to study non linear stability of stratified flow models, and analyze asymptotic regimes for which the system tends to another sharp interface model close to the so called four equations model for incompressible two phase flows (Collaboration with D. Lannes (ENS Paris) and J.-C. Saut (Université Paris Sud)). Linear stability conditions on Richardson number can be handled by Hamiltonian methods (Holm, Marsden, Ratiu, Weinstein, Phys Rep 123 (1985) no 3) under restrictive assumptions on high frequencies of density perturbations. One of the objectives of this work is to understand those results by using hyperbolic techniques in the framework of internal gravity waves.
- Compressible two phase models
Complex flows in the presence of two phases with their own density, velocity and energy are of great industrial importance (nuclear industry, combustion problems…), though still not well understood from a theoretical point of view. One of the objectives of this long term research program (started at CEA in collaboration with ENS Cachan in the early 2000’s) is to address the asymptotic behavior of such models in the low Mach number regime (Collaboration with D. Bresch (Université de Chambéry), J.-M. Ghidaglia (ENS Cachan), E. Grenier (ENS Lyon)). The monthly working group on « Multiphase Flows » at CMLA of ENS Cachan leads to particularly fruitful related discussions.
- Oil reservoir models
Understanding of mathematical properties of multiphase flows in porous media for oil and gas reservoirs still remains to be improved. Such models implemented in industrial simulation software can be used with or without capillary pressure. Such additional pressure leads to degenerate parabolicity properties which have been extensively studied for the past two decades. Recent results by C. Galusinski and M. Saad (A nonlinear degenerate system modeling water-gas flows in porous media, DCDS B Vol. 9, N. 2 (2008)) are a significant step towards global existence result for the “famous Black Oil model” commonly used in the Oil and Gas Industry under some particular closure assumptions involving capillary pressures and relative permeabilities. In the absence of capillary pressures, pseudo differential operators theory, used in the framework of compressible Euler and Navier Stokes flows in the low Mach number regime, can be adapted to prove local in time existence and uniqueness of smooth solutions (collaboration with D.Bresch (Université de Chambéry), E. Grenier (ENS Lyon)).