Filtered Hyperbolic Moment Method for the Vlasov Equation

In this paper, we investigate the effect of the filter for the hyperbolic moment equations (HME) (Cai et al. in Commun Pure Appl Math 67(3):464–518, 2014; Cai et al. in SIAM J Sci Comput 35(6):A2807–A2831, 2013) of the Vlasov–Poisson equations and propose a novel quasi time-consistent filter to suppress the numerical recurrence effect. By taking properties of HME into consideration, the filter preserves a lot of physical properties of HME, including Galilean invariance and conservation of mass, momentum and energy. We present two viewpoints—collisional viewpoint and dissipative viewpoint—to dissect the filter, and show that the filtered hyperbolic moment method can be treated as a solver of the Vlasov equation. Numerical simulations of the linear Landau damping and two stream instability demonstrate the effectiveness of the filter in restraining recurrence arising from particle streaming. Both the analysis and the numerical results indicate that the filtered method can capture the evolution of the Vlasov equation, even when phase mixing and filamentation dominate.