A 9-bit multiple relaxation Lattice Boltzmann magnetohydrodynamic algorithm for 2D turbulence

While a minimalist representation of 2D Magnetohydrodynamics (MHD) on a square lattice is a 9-bit scalar and 5-bit vector distribution functions, here we examine the effect of using the 9-bit vector distribution function on the effect of a magnetic field on the Kelvin–Helmholtz instability. While there is little difference in the simulation results between the 5-bit and the 9-bit vector distribution models in the vorticity, energy spectra, etc., the 9-bit model permits simulations with mean magnetic field a factor of approximately 2 greater than those attainable in the standard 5-bit model. Indeed a 9-bit single-relaxation model can attain such success over a 5-bit multiple-relaxation model at the same computational expense.