Numerical dissipation induced by the low-pass filtering in nonlinear gyrokinetic 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 the 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 of accuracy, where Np is the number of filter points. Numerical results after applying the optimized low-pass filtering to the nonlinear gyrokinetic turbulence simulation suggest that the nine-point format preserves intact mesoscopic zonal structures in tokamak plasma, and is therefore suitable for long-time nonlinear turbulence simulations.