In this paper, we investigate the effect of the filter for the hyperbolicmoment equations(HME) [15] of the Vlasov-Poisson equations and propose a novelquasi time- consistent filter to suppress the numerical recurrence effect. Bytaking properties of HME into consideration, the filter preserves a lot ofphysical properties of HME, including Galilean invariance and the conservationof mass, momentum and energy. We present two viewpoints, collisional viewpointand dissipative viewpoint, to dissect the filter, and show that the filteredhyperbolic moment method can be treated as a solver of Vlasov equation.Numerical simulations of the linear Landau damping and two stream instabilityare tested to demonstrate the effectiveness of the filter in restrainingrecurrence arising from particle streaming. Both the analysis and the numericalresults indicate that the filtered HME can capture the evolution of the Vlasovequation, even when phase mixing and filamentation are dominant.
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