We discretize the Vlasov-Poisson system using conservative semi-Lagrangian (CSL) discontinuous Galerkin (DG) schemes that are asymptotic preserving (AP) in the quasi-neutral limit. The proposed method (CSLDG) relies on two key ingredients: the CSLDG discretization and a reformulated Poisson equation (RPE). The use of the CSL formulation ensures local mass conservation and circumvents the Courant-Friedrichs-Lewy condition, while the DG method provides high-order accuracy for capturing fine-scale phase space structures of the distribution function. The RPE is derived by the Poisson equation coupled with moments of the Vlasov equation. The synergy between the CSLDG and RPE components makes it possible to obtain reliable numerical solutions, even when the spatial and temporal resolution might not fully resolve the Debye length. We rigorously prove that the proposed method is asymptotically stable, consistent and satisfies AP properties. Moreover, its efficiency is maintained across non-quasi-neutral and quasi-neutral regimes. These properties of our approach are essential for accurate and robust numerical simulation of complex electrostatic plasmas. Several numerical experiments verify the accuracy, stability and efficiency of the proposed CSLDG schemes.

翻译：本文采用在准中性极限下具有渐近保持特性的守恒半拉格朗日间断伽辽金格式对Vlasov-Poisson系统进行离散化。所提出的CSLDG方法基于两个核心要素：CSLDG离散格式与重构泊松方程。采用守恒半拉格朗日表述确保了局部质量守恒并规避了Courant-Friedrichs-Lewy条件限制，而间断伽辽金方法为捕捉分布函数相空间精细结构提供了高阶精度。重构泊松方程通过泊松方程与Vlasov方程矩耦合推导得出。CSLDG与重构泊松方程的协同作用使得即使在时空分辨率未能完全解析德拜长度的条件下，仍能获得可靠的数值解。我们严格证明了所提方法具有渐近稳定性、相容性并满足渐近保持特性。此外，该方法在非准中性与准中性区域均能保持计算效率。这些特性对于复杂静电等离子体的精确鲁棒数值模拟至关重要。系列数值实验验证了所提CSLDG格式的精度、稳定性与计算效率。