Accelerating the simulation of kinetic shear Alfv\'en waves with a dynamical low-rank approximation

TL;DR

This paper introduces a dynamical low-rank algorithm for gyrokinetic plasma models, significantly reducing computational costs while accurately capturing wave dispersion, demonstrated through shear Alfvén wave simulations.

Contribution

The paper develops a novel low-rank approximation method tailored for gyrokinetic models, enabling efficient and accurate simulation of plasma waves with reduced computational resources.

Findings

Exact dispersion relation recovery at rank 1

Order of magnitude reduction in computation time and memory

Effective comparison of different integrators and discretizations

Abstract

We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe strongly magnetized plasmas. The low-rank approximation is based on a decomposition into variables parallel and perpendicular to the magnetic field, as suggested by the physics of the underlying problem. We show that the resulting scheme exactly recovers the dispersion relation even with rank 1. We then perform a simulation of kinetic shear Alfv\'en waves and show that using the proposed dynamical low-rank algorithm a drastic reduction (multiple orders of magnitude) in both computational time and memory consumption can be achieved. We also compare the performance of robust first and second-order projector splitting, BUG (also called unconventional), and augmented BUG integrators as well as a FFT-based spectral and Lax--Wendroff discretization.