Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemesfor simulating a variety of physical systems. In this paper a newlattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensionalincompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. Thecompressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is thenapplied to the Hartmann flow, giving reasonable results.