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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.

We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh–Taylor turbulence with a Shan–Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

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