AI 中文总结
针对准中性和低马赫数等离子体模拟，提出一种保渐近微-宏格式，通过耦合极限、引入辅助变量等设计，解决低马赫刚性问题，数值实验验证其可保持低马赫数平衡。
AI 中文摘要
我们提出一种保渐近的微-宏方法，该方法衔接电子的动力学描述与一种简化的低频模型，其中电子为无质量、满足玻尔兹曼关系的准中性流体。该构造有两个显著特征：其一，流体极限与低马赫极限相耦合，从而在宏观系统上处理低马赫刚性，宏观系统可采用隐式处理，而非在动力学方程上处理；其二，引入辅助变量对刚性力平衡进行重标度，将奇异的低马赫极限转化为增广系统的正则极限，且该增广系统在德拜长度下保持一致非退化。这对离散层面至关重要：采用迭代线性求解器时，小马赫数引发的刚性会放大求解器残差，因此仅在时间离散上设计为保渐近的格式，一旦考虑完整求解链，便会丧失该特性。所提格式可保留保渐近特性，且无需随马赫数减小而收紧求解器容差，还存在一种后处理变体，可解耦辅助变量并减小线性系统规模。涵盖不同参数区域的数值实验验证了该分析：标准半隐式格式会在残差放大下丧失低马赫数平衡，而所提格式可将该平衡保持至舍入误差级别。
英文摘要
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.
