  In this paper, we investigate the effect of the filter for the hyperbolic
moment equations(HME) [15] 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 the 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 Vlasov equation.
Numerical simulations of the linear Landau damping and two stream instability
are tested to demonstrate the effectiveness of the filter in restraining
recurrence arising from particle streaming. Both the analysis and the numerical
results indicate that the filtered HME can capture the evolution of the Vlasov
equation, even when phase mixing and filamentation are dominant.
