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

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.