One-stage simplified lattice Boltzmann method for two- and three-dimensional magnetohydrodynamic flows

Abstract

In this paper, we propose a new simplified lattice Boltzmann method (SLBM) for magnetohydrodynamic flows that outperforms the classical one in terms of accuracy, while preserving its advantages. A very recent paper [A. De Rosis, J. Al-Adham, H. Al-Ali and R. Meng, "Double-D2Q9 lattice Boltzmann models with extended equilibrium for two-dimensional magnetohydrodynamic flows", Phys. Fluids 33, 035143 (2021)] demonstrated that the SLBM enforces the divergence-free condition of the magnetic fiield in an excellent manner and involves the lowest amount of virtual memory. However, the SLBM is characterised by the poorest accuracy. Here, the two-stages algorithm that is typical of the SLBM is replaced by a one-stage procedure following the approach devised for non-conductive fluids in a very recent effort [A. Delgado-Gutierrez, P. Marzocca, D. Cardenas, and O. Probst, "A single-step and simplified graphics processing unit lattice Boltzmann method for high turbulent flows", International Journal for Numerical Methods in Fluids ( 2021)]. The Chapman-Enskog expansion formally demonstrates the consistency of the present scheme. The resultant algorithm is very compact and easy to be implemented. Given all these features, we believe that the proposed approach is an excellent candidate to perform numerical simulations of two-and three-dimensional magnetohydrodynamic flows.

Statistical properties of three-dimensional Hall magnetohydrodynamics turbulence

“…Furthermore, it will be interesting to examine Hall-MHD flows by generalizing the studies in the following lattice Boltzmann models (LBM) papers on MHD flows that have appeared recently. 76…”

Turbulence suppression and regeneration in a magnetohydrodynamic duct flow due to influence of arbitrary electrically conductive walls

“…Compressible MHD turbulence was studied by Yang et al 26 The authors investigated which turbulence theories proposed for the incompressible cases would be also valid for compressible cases. An alternative approach to simulate magnetohydrodynamic flows, namely, the one-stage simplified lattice Boltzmann method, was proposed by De Rosis et al 27 The accuracy and computational efficiency of this method were demonstrated, making it a good alternative approach for predicting MHD flows.…”