Numerical dissipation induced by the low-pass filtering in nonlinear gyrokinetic simulations

TL;DR

This paper analyzes how low-pass filtering used for de-aliasing in nonlinear gyrokinetic simulations introduces numerical dissipation, and demonstrates an optimized filtering approach that preserves key plasma structures for long-term simulations.

Contribution

It provides an analytical understanding of dissipation caused by low-pass filters and proposes an optimized filter that maintains important plasma features in gyrokinetic turbulence simulations.

Findings

Long-wave dissipation coefficient scales with (Np-3) power of wavenumber.

Nine-point filter preserves mesoscopic zonal structures.

Optimized filtering enables long-time turbulence simulations.

Abstract

De-aliasing is an essential procedure for eliminating the aliasing error in nonlinear simulations, such as nonlinear gyrokinetic turbulence simulations. An ideal approach to de-aliasing in the periodic dimension is Fourier truncation. Finite difference low-pass filtering applied in the non-periodic direction strongly dampens aliasing modes. At the same time, it induces numerical dissipation in the region of the physically realistic solution. It is shown analytically that the long-wave dissipation coefficient is proportional to the (Np-3) power of the wavenumber under desirable constraints satisfying the highest order accuracy, where Np is the number of filter points. Numerical results after applying the optimised low-pass filtering to the nonlinear gyrokinetic turbulence simulation suggest that the nine-point format preserves intact mesoscopic zonal structures in Tokamak plasmas, and is therefore suitable for long-time nonlinear turbulence simulations.