Asymptotic preserving schemes for the Wigner–Poisson–BGK equations in the diffusion limit.

Abstract: This work focuses on the numerical simulation of the Wigner–Poisson–BGK equation in the diffusion asymptotics. Our strategy is based on a “micro–macro” 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 Wigner–Poisson equation in the collisionless regime. Numerical experiments confirm the good behavior of the numerical scheme in both regimes. The case of a spatially dependent is also investigated. [Copyright &y& Elsevier]