# A Partial Entropic Stabilization of Lattice Boltzmann MHD

## TL;DR

This paper introduces a partial entropic stabilization method for lattice Boltzmann magnetohydrodynamics, improving simulation stability and accuracy in 2D MHD problems like Kelvin-Helmholtz instability.

## Contribution

It extends the entropic lattice Boltzmann method to MHD by applying it only to the scalar distribution, enabling better handling of magnetic field reversals.

## Key findings

- Achieved very good simulation results for MHD instabilities.
- Benchmarking shows improved stability over previous models.
- Successfully applied to complex 2D MHD phenomena.

## Abstract

The entropic lattice Boltzmann algorithm of Karlin et. al. is partially extended to magnetohydrodynamics, based on the Dellar model of introducing a vector distribution for the magnetic field. This entropic ansatz is now applied only to the scalar particle distribution function so as to permit the many problems entailing magnetic field reversal. A 9-bit lattice is employed for both particle and magnetic distributions for our two dimensional simulations. The entropic ansatz is benchmarked against our earlier multiple relaxation lattice-Boltzmann model for the Kelvin-Helmholtz instability in a magnetized jet. Other two dimensional simulations are performed and compared to results determined by more standard direct algorithms: in particular the switch over between the Kelvin-Helmholtz/tearing mode instability of Chen et. al., and the generalized Orszag-Tang vortex model of Biskamp-Welter. Very good results are achieved.