Section: New Results
Asymptotic preserving schemes
Participant : Nicolas Crouseilles.
In [18] , we extend the micro-macro decomposition
based numerical schemes developed previously to the collisional
Vlasov-Poisson model in the diffusion and high-field asymptotics.
In doing so, we first write the Vlasov-Poisson model as a system that
couples the macroscopic (equilibrium) part with the remainder part.
A suitable discretization of this micro-macro model enables to derive
an asymptotic preserving scheme in the diffusion and high-field asymptotics.
In addition, two main improvements are presented: On the one hand a
self-consistent electric field is introduced, which induces a specific
discretization in the velocity direction, and represents a wide range of
applications in plasma physics. On the other hand, as suggested
in a previous reference, we introduce a suitable reformulation of the
micro-macro scheme which leads to an asymptotic preserving
property with the following property: It degenerates into an
implicit scheme for the diffusion limit model when
In [45] , a Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field is derived. This consists in writing the solution of this equation as a sum of two oscillating functions with circonscribed oscillations. The first of these functions has a shape which is close to the shape of the Two-Scale limit of the solution and the second one is a correction built to offset this imposed shape.