Abstract In this paper, the discrete unified gas kinetic scheme (DUGKS), which is a novel direct kinetic method, is developed for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes characterized by a wide range of Knudsen number and normalized Debye length. The current scheme is constructed for multiscale plasma simulation, while the temporal and spatial step sizes of the method are not restricted by the Knudsen number and normalized Debye length. One key feature of this method is the un-splitting treatment of the particle transport, collision and acceleration in both the distribution function evolution and the numerical flux evaluation, which enables the method to economically and accurately provide a satisfactory solution for all Knudsen number regimes. With the coupling of the appropriate time discretization of the distribution function and a reformulated Poisson equation, the method further provides an easy-to-implement and efficient way for the investigation of electrical potential in all normalized Debye regimes. As a result, the proposed DUGKS becomes an asymptotic preserving scheme, which automatically degenerates to be consistent with the discretization of corresponding limiting models. Several numerical experiments in different electrostatic plasma regimes are presented to validate the proposed method.

中文翻译：

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在所有静电等离子体状态下重新制定的 BGK-Vlasov-Poisson 系统的离散统一气体动力学方案

摘要 在本文中，离散统一气体动力学方案 (DUGKS) 是一种新颖的直接动力学方法，它是针对所有静电等离子体状态下重新制定的 BGK-Vlasov-Poisson 系统开发的，该系统具有宽范围的 Knudsen 数和归一化德拜长度。当前方案是为多尺度等离子体模拟而构建的，而该方法的时间和空间步长不受克努森数和归一化德拜长度的限制。该方法的一个关键特征是在分布函数演化和数值通量评估中对粒子输运、碰撞和加速进行了不分裂处理，这使得该方法能够经济而准确地为所有 Knudsen 数制度提供令人满意的解决方案。通过将分布函数的适当时间离散化与重新制定的泊松方程相结合，该方法进一步提供了一种易于实施且有效的方法，用于研究所有归一化德拜机制中的电势。因此，提出的 DUGKS 成为渐近保持方案，它自动退化以与相应限制模型的离散化一致。提出了在不同静电等离子体状态下的几个数值实验来验证所提出的方法。自动退化为与相应限制模型的离散化一致。提出了在不同静电等离子体状态下的几个数值实验来验证所提出的方法。自动退化为与相应限制模型的离散化一致。提出了在不同静电等离子体状态下的几个数值实验来验证所提出的方法。