Simulating background shear flow in local gyrokinetic simulations

TL;DR

This paper identifies issues with the wavevector-remap method in local gyrokinetic simulations, demonstrates its inaccuracies, and proposes a corrected scheme that improves the physical fidelity of simulation results.

Contribution

The authors derive a new, simple method for incorporating background shear flow in Fourier-space gyrokinetics and demonstrate its advantages over the traditional wavevector-remap approach.

Findings

Wavevector-remap introduces unphysical smeared mode coupling.

The corrected scheme reduces numerical artifacts and improves convergence.

Original remap scheme does not converge as system size increases.

Abstract

Local gyrokinetic simulations solve the gyrokinetic equations with homogeneous background gradients, typically using a doubly periodic domain in the (x,y) plane (i.e. perpendicular to the field line). Spatial Fourier representations are almost universal in local gyrokinetic codes, and the wavevector-remap method was introduced in [Hammett et. al., Bull Am Phys Soc VP1 136, (2006)] as a simple method for expressing the local gyrokinetic equations with a background shear flow in a Fourier representation. Although extensively applied, the wavevector-remap method has not been formally shown to converge, and suffers from known unphysicality when the solutions are plotted in real space [Fox et. al. PPCF 59, 044008]. In this work, we use an analytic solution in slab geometry to demonstrate that wavevector-remap leads to incorrect smeared non-linear coupling between modes. We derive a correct, relatively simple method for solving local gyrokinetics in Fourier space with a background shear flow, and compare this to the wavevector-remap method. This allows us to show that the error in wavevector-remap can be seen as an incorrect rounding in wavenumber space in the nonlinear term. By making minor modifications to the nonlinear term, we implement the corrected wavevector-remap scheme in the GENE[25] code and compare results of the original and corrected wavevector-remap for standard nonlinear benchmark cases. Certain physical phenomena are impacted by the errors in the original remap scheme, and these numerical artefacts do not reduce as system size increases: that is, original wavevector-remap scheme does not converge to the correct result.