In this paper, we present a novel finite-volume direct kinetic method, the so-called discrete unified gas kinetic scheme (DUGKS), for electrostatic plasma. One key feature of this method is the semi-implicit un-splitting treatment of particle transport and collision, thus the time step in current DUGKS is not limited by the particle collision time. In addition, a fourth order compact MUSCL scheme with a positivity preserving limiter is implemented in the interface reconstruction, which enables present DUGKS to preserve the favorable conservative property and positivity of distribution function. Combined with this MUSCL method, the Semi-Lagrangian scheme is used for the particle transport in velocity space to remove CFL restriction induced by the large electric force. As a result, the proposed DUGKS becomes an efficient and stable multiscale scheme. Several numerical experiments, including plasma sheath, linear Landau damping, collisional nonlinear Landau damping and plasma ion acceleration, are performed to validate current DUGKS. A comparative study of current DUGKS with a general particle in cell (PIC) method which could handle particle collision in a conservative way is also presented. Theory and numerical experiments demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes, while the PIC method is desired for the field-{ dominated} plasma flows involving a wide range of {velocities}.

中文翻译：

---

静电等离子体的离散统一气体动力学方案及其与粒子内方法的比较

在本文中，我们提出了一种新颖的有限体积直接动力学方法，即用于静电等离子体的所谓离散统一气体动力学方案（DUGKS）。该方法的一个关键特征是对粒子传输和碰撞的半隐式不分裂处理，因此当前DUGKS中的时间步长不受粒子碰撞时间的限制。此外，在接口重构中实现了具有正性保留限制器的四阶紧凑型MUSCL方案，这使得当前的DUGKS能够保留良好的保守性和正态分布函数。结合这种MUSCL方法，使用半拉格朗日方法在速度空间中进行粒子传输，以消除由大电力引起的CFL限制。结果，提出的DUGKS成为一种有效且稳定的多尺度方案。进行了一些数值实验，包括等离子体鞘，线性Landau阻尼，碰撞非线性Landau阻尼和等离子体离子加速，以验证当前的DUGKS。还介绍了当前的DUGKS与普通粒子在细胞内（PIC）方法的比较研究，该方法可以以保守的方式处理粒子碰撞。理论和数值实验表明，对于涉及小静电扰动和高碰撞态的等离子体流，优选DUGKS，而对于涉及{速度}范围广泛的以场为主导的等离子体流，则需要PIC方法。还介绍了当前的DUGKS与普通粒子在细胞内（PIC）方法的比较研究，该方法可以以保守的方式处理粒子碰撞。理论和数值实验表明，对于涉及小静电扰动和高碰撞态的等离子体流，优选DUGKS，而对于涉及{速度}范围广泛的以场为主导的等离子体流，则需要PIC方法。还介绍了当前的DUGKS与普通粒子在细胞内（PIC）方法的比较研究，该方法可以以保守的方式处理粒子碰撞。理论和数值实验表明，对于涉及小静电扰动和高碰撞态的等离子体流，优选DUGKS，而对于涉及{速度}范围广泛的以场为主导的等离子体流，则需要PIC方法。