Double Multiple-Relaxation-Time model of Lattice-Boltzmann Magnetohydrodynamics at Low Magnetic Reynolds Numbers

TL;DR

This paper introduces a new lattice-Boltzmann method using multiple relaxation times for magnetohydrodynamics at low magnetic Reynolds numbers, improving stability and boundary handling in simulations of MHD pipe flows.

Contribution

It develops a novel multi-relaxation-time lattice-Boltzmann scheme for MHD, addressing stability issues of previous models and providing better boundary condition implementation.

Findings

Enhanced stability of MHD simulations with the new model

Successful application to transient pipe flow scenarios

Improved boundary condition handling on curved surfaces

Abstract

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on a manifestly Galilean covariant modeling of the Navier-Stokes equations. The simulation of the magnetic induction equation within the lattice-Boltzmann approach to MHD has been usually devised along the lines of the simplest phenomenological description, the single relaxation time (SRT) model. In order to deal with well-known stability difficulties of the SRT framework, we introduce, alternatively, a multi-relaxation-time technique for the solution of the magnetic induction equation, combined with a novel boundary condition method to cope with the subtleties of magnetic Boltzmann-like distributions on curved boundaries. As an application, we investigate open issues related to the description of transient flow regimes in MHD pipe flows, subject to non-uniform magnetic fields.