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 the central-moment (CM) and multi-relaxation-time (MRT) collision models. 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 to solve the complete induction equation. In order to deal with well-known stability difficulties of the SRT framework for larger magnetic relaxation time scales, we introduce, alternatively, a MRT technique for the solution of the magnetic induction equation, which proves to be efficient in extending the domain of applicability of the lattice-Boltzmann method to MHD problems. We also put forward a novel and practical boundary condition method to cope with the subtleties of magnetic Boltzmann-like distributions on curved boundaries. As supporting applications, we discuss the performance of the CM–MRT algorithm to describe the complex dynamics of the 3D Orszag–Tang vortex problem and open issues related to transient flow regimes in MHD pipe flows, subject to uniform and non-uniform magnetic fields.