Lattice Boltzmann formulation for Braginskii magnetohydrodynamics

Braginskii magnetohydrodynamics is a single-fluid description of large-scale motions in a strongly magnetised plasma, one in which the ion gyroradius is much smaller than the mean free path between collisions in an unmagnetised plasma of the same density and temperature. The relation between stress and strain rate then becomes highly anisotropic, with the viscous stress being predominantly aligned parallel to the magnetic field lines. We modify an existing lattice Boltzmann formulation of isotropic resistive magnetohydrodynamics to simulate Braginskii magnetohydrodynamics by introducing an anisotropic collision operator for the hydrodynamic distribution functions. This collision operator applies a different relaxation time to the component of stress directed parallel to the magnetic field. The method is illustrated by comparison with independent numerical solutions for steady planar channel flows.