Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations
For researchers using Hermite-spectral methods for transport equations, this provides a theoretical justification for suppressing unphysical recurrence, though the analysis is limited to specific models.
The paper analyzes and proves that filters exponentially damp non-constant modes in Hermite-spectral simulations of transport equations, without affecting the damping rate of electric energy in linear Landau damping. Numerical tests confirm the filter's effectiveness.
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.