Filtered Hyperbolic Moment Method for the Vlasov Equation

TL;DR

This paper introduces a novel quasi time-consistent filter for hyperbolic moment equations of the Vlasov-Poisson system, effectively suppressing numerical recurrence while preserving key physical properties.

Contribution

It proposes a new filter that maintains physical invariants and enhances the hyperbolic moment method's ability to simulate Vlasov dynamics accurately.

Findings

The filter suppresses recurrence in linear Landau damping simulations.

It preserves physical invariants like mass, momentum, and energy.

The method accurately captures phase mixing and filamentation effects.

Abstract

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.