AN ASYMPTOTIC PRESERVING SCHEME BASED ON A MICRO-MACRO DECOMPOSITION FOR COLLISIONAL VLASOV EQUATIONS: DIFFUSION AND HIGH-FIELD SCALING LIMITS

作者：Crouseilles Nicolas^*; Lemou Mohammed

来源：Kinetic and Related Models, 2011, 4(2): 441-477.

DOI：10.3934/krm.2011.4.441

• Vlasov equation
• BGK equation
• drift-diffusion equation
• high-field equation
• Chapman-Enskog expansion
• asymptotic preserving schemes
• micro-macro decomposition

In this work, we extend the micro-macro decomposition based numerical schemes developed in [3] 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 [30], 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 epsilon -> 0, which makes it free from the usual diffusion constraint Delta t = (sic)(Delta x(2)) in all regimes. Numerical examples are used to demonstrate the efficiency and the applicability of the schemes for both regimes.

• 出版日期2011-6
• 单位INRIA