# A large eddy lattice Boltzmann simulation of magnetohydrodynamic turbulence

## TL;DR

This paper presents large eddy simulations of magnetohydrodynamic turbulence using an extended lattice Boltzmann model, demonstrating good agreement with direct numerical simulations for the Kelvin-Helmholtz instability.

## Contribution

It introduces a novel LES approach for LB-MHD that incorporates non-commuting perturbations and physical constraints for subgrid modeling.

## Key findings

- Simulations agree well with direct numerical results.
- The method effectively captures magnetized Kelvin-Helmholtz instability.
- Extension of LB-MHD to LES with non-commuting perturbations.

## Abstract

Large eddy simulations (LES) of a lattice Boltzmann magnetohydrodynamic (LB-MHD) model are performed for the unstable magnetized Kelvin-Helmholtz jet instability. This algorithm is an extension of Ansumali et. al. (2004) to MHD in which one performs first an expansion in the filter width on the kinetic equations followed by the usual low Knudsen number expansion. These two perturbation operations do not commute. Closure is achieved by invoking the physical constraint that subgrid effects occur at transport time scales. The simulations are in very good agreement with direct numerical simulations.