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

作者：Crouseilles Nicolas^*; Manfredi Giovanni

来源：Computer Physics Communications, 2014, 185(2): 448-458.

DOI：10.1016/j.cpc.2013.06.002

• Wigner equation
• Diffusion limit
• Asymptotic preserving schemes

This work focuses on the numerical simulation of the Wigner-Poisson-BGK equation in the diffusion asymptotics. Our strategy is based on a %26quot;micro-macro%26quot; 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 e (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 e(x) is also investigated.

• 出版日期2014-2