Numerical methods for kinetic equations under different regimes

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Résumé : In this talk we will discuss the construction of high order numerical methods for solving non linear kinetic equations under different regimes. First part of the talk will be devoted to a short introduction to the problem, to the different scaling encountered in applications and to the relative numerical challenges. In particular, we will consider the hydrodynamic, the diffusion and the quasi neutral scaling arising in plasma physics simulations.
In a second part we will introduce a general framework which can be used to solve multiscale problems and which guarantees uniform stability and accuracy for all the different regimes studied. In a last part we will discuss efficient techniques which permit to couple this class of schemes for kinetic models to the corresponding macroscopic models in a domain decomposition fashion.