Filtered Hyperbolic Moment Method for the Vlasov Equation
This work addresses the recurrence problem in kinetic plasma simulations, offering a filtered HME method that maintains physical properties for practitioners using moment-based approaches.
The paper introduces a quasi time-consistent filter for hyperbolic moment equations (HME) to suppress numerical recurrence in Vlasov-Poisson simulations, preserving Galilean invariance and conservation laws. Numerical tests on linear Landau damping and two-stream instability show the filter effectively captures Vlasov evolution even with strong phase mixing.
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.