Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations

TL;DR

This paper analyzes and proves the effectiveness of filters in suppressing unphysical recurrence in Hermite-spectral methods for transport equations, supported by numerical tests.

Contribution

It provides a rigorous mathematical analysis of how filters damp non-constant modes and demonstrates their impact on transport equation simulations.

Findings

Filters exponentially damp non-constant modes

Filters do not affect electric energy damping rate

Numerical tests confirm filter effectiveness

Abstract

We study the unphysical recurrence phenomenon arising in the numerical simulation of the transport equations using Hermite-spectral method. From a mathematical point of view, the suppression of this numerical artifact with filters is theoretically analyzed for two types of transport equations. It is rigorously proven that all the non-constant modes are damped exponentially by the filters in both models, and formally shown that the filter does not affect the damping rate of the electric energy in the linear Landau damping problem. Numerical tests are performed to show the effect of the filters.