Asymptotic-Preserving methods and multiscale models for plasma physics

The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non-magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.