Entropic Lattice Boltzmann Simulations of MHD Turbulence

Lattice Boltzmann (LB) codes are ideal to study MHD turbulence since it is a mesoscopic algorithm in a higher dimensional space but whose solution in that space is far simpler to achieve that direct CFD algorithms. In particular, one is no longer hand-cuffed by fast magnetoacoustic waves which are sometimes filtered out by an anelastic approximation. Moreover, these LB simulations can enforce div B = 0 automatically since this arises as the trace of an asymmetric tensor. However the achievable Reynolds and magnetic Reynolds numbers are restricted by numerical instabilities. Here we consider entropic formulations of LB for MHD. For Navier-Stokes turbulence, an entropic scheme has permitted fully resolved simulations on 1600 x 1600 x 1600 spatial grid at a Reynolds number of 25 000.