Multi-scale kinetic scheme for the collisional Vlasov-Poisson system

We propose a multiscale kinetic scheme for a collisional Vlasov Poisson (VP) system. In order to capture non-equilibrium state of the distribution function, the unified gas kinetic scheme (UGKS) has been used for the construction of the numerical solution for the system. Due to the periodic boundary condition, the Poisson equation for electric field is solved by the fast Fourier transform (FFT) method. By combining the UGKS and FFT, a robust scheme for the collisional VP system has been obtained. The present scheme is able to accurately capture the numerical solutions in both kinetic and diffusive regimes. This scheme is asymptotic preserving with the variation of the ratio between the mean free path and the numerical cell size. Numerical tests validate the efficiency and accuracy of the scheme.