Discrete unified gas kinetic scheme for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes

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.