Nicolas Crouseilles

Micro-macro decomposition for collisional Vlasov-Poisson equations

Abstract:
Using the micro-macro decomposition introduced recently, we derive
asymptotic preserving schemes for the collisional Vlasov-Poisson equation
in two different regimes, the diffusion and the high-field asymptotics.
The so-obtained scheme are stable with respect to the small parameter
and, at the fully discrete level, it is shown that the numerical scheme
degenerates into a consistent discretization of the continuous asymptotic model,
up to the second order of the Chapman-Enskog expansion.