Asymptotic preserving schemes for the WignerPoissonBGK equations in the diffusion limit
This work focuses on the numerical simulation of the WignerPoissonBGK equation in the diffusion asymptotics. Our strategy is based on a micromacro decomposition, which leads to a system of equations that couple the macroscopic evolution (diffusion) to a microscopic kinetic contribution for the fluctuations. A semi-implicit discretization provides a numerical scheme which is stable with respect to the small parameter ? ? (mean free path) and which possesses the following properties: (i) it enjoys the asymptotic preserving property in the diffusive limit; (ii) it recovers a standard discretization of the WignerPoisson equation in the collisionless regime. Numerical experiments confirm the good behavior of the numerical scheme in both regimes. The case of a spatially dependent ?(x) ? ( x ) is also investigated.
asymptotic preserving schemes diffusion limit wigner equation