An Asymptotic-Preserving Micro--Macro Scheme for Plasma Simulations in Quasi-Neutral and Low-Mach-Number Regimes with Kinetic Upgrades

Abstract

We propose an asymptotic-preserving micro--macro method bridging a kinetic description of electrons and a low-frequency reduced model in which the electrons are a massless, quasi-neutral fluid obeying the Boltzmann relation. Two features distinguish the construction. First, the fluid and low-Mach limits are coupled, so that the low-Mach stiffness is handled on a macroscopic system, where implicit treatment is affordable, rather than on the kinetic equations. Second, an auxiliary variable rescales the stiff force balance, turning the singular low-Mach limit into a regular limit of the augmented system, which is shown to remain non-degenerate uniformly in the Debye length as well. This matters at the discrete level: with an iterative linear solver, the stiffness induced by the small Mach number amplifies the solver residual, so that a scheme designed to be asymptotic-preserving in its time discretization alone loses that property once the full solution chain is taken into account. The proposed scheme retains it, with no tightening of the solver tolerance as the Mach number vanishes, and admits a post-processing variant that decouples the auxiliary variable and reduces the size of the linear system. Numerical experiments spanning distinct parameter regimes confirm the analysis: standard semi-implicit schemes lose low-Mach-number equilibrium under residual amplification, whereas the proposed schemes preserve it down to round-off.