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

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 [De Rosis et al., “Double-D2Q9 models with extended equilibrium two-dimensional flows,” Phys. Fluids 33, 035143 (2021)] demonstrated SLBM enforces divergence-free condition magnetic field an excellent manner and involves lowest amount virtual memory. However, is characterized by poorest accuracy. Here, two-stage algorithm typical replaced one-stage procedure following approach devised non-conductive fluids effort [Delgado-Gutierrez “A single-step graphics processing unit high turbulent Int. J. Numer. Methods 93, 2339 (2021)]. The Chapman–Enskog expansion formally demonstrates consistency present scheme. resultant compact easily implemented. Given all these features, believe proposed candidate to perform numerical simulations two- three-dimensional flows.