I am an “applied mathematician”. Roughly speaking my research activity is devoted to PDEs emanating from physics. A tentative list of keywords could be: Kinetic equations, Hyperbolic equations, Hydrodynamic limit, Diffusion approximation, Homogenization (deterministic or random), Fluid mechanics, Scientific computing, Asymptotic preserving schemes
To be more specific, I am interested in models describing a large number of particles subject to various interaction phenomena and I wish to describe the influence of microscopic scales on the macroscopic observation scales. This naturally leads to questions of asymptotic analysis. The adopted viewpoint is not restricted to an application and the word “particles” might cover several physical situations: neutrons in a nuclear core, photons around a star, self-graviating planetary systems, electrons and ions in a semiconductor device or in spacial plasmas, or even bacteria…
The particles can be described through the evolution of their distribution function in phase space, it is the viewpoint of statistical physics due to L. Boltzmann (which explains the tribute with the small pics). This work can be related to the 6th Hilbert's problem. The analysis of these problems relies on discussion of the modeling issues and naturally leads to problems of numerical analysis in order to design specific methods able to treat correctly, but for a still reasonable computational cost, the various scales involved in the problem. Recently, I pay attention to problems related to the numerical simulation of complex fluid flows, characterized by heterogeneous densities. Applications rely for instance to the modeling of mixtures, pollutant transport, avalanches… People interested in this topic are invited to play with NS2DDV, an OpenSource code dedicated to the simulation of 2D incompressible viscous flows.