Research objectives and content
We are interested in boundary layers problems that are of particular interest in plasma physics. These problems lead to the study of singular perturbations for the Vlasov-Poisson system, when a kinetic description is used for the plasma, or for the Euler-Poisson system, when a fluid model is considered. The first stage concerns the one dimensional stationary case. Then we will turn to the modelling of the evolution problem. This is the core of our project: the different phenomena call for a multiple time scale analysis and pose interesting mathematical problems such as Euler-Poisson system resolution. Next, a numerical code will be developed that will treat the unstationary system. Finally we will study the derivation and numerical implementation of multidimensional models. Training content (objective, benefit and expected impact)
Through this project, I will have to deal with all the aspects of applied mathematics: modelling, analytical study and numerical simulation. Also, I have a unique opportunity to share the great expertise that researchers at CMAP have acquired on this subject.
Links with industry / industrial relevance (22)
The simulation of plasma devices is becoming an important industrial issue. We are in contact with Sollac, Thomson, Pirelli and St. Gobain Recherche who are very interested in our numerical codes.