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Lattice Boltzmann formulation for Braginskii magnetohydrodynamics

P. J. Dellar (2010) Lattice
Boltzmann formulation for Braginskii magnetohydrodynamics (in
press) Computers & Fluids

Preprint available as a PDF ( ICFD_Braginskii.pdf
116K)

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Abstract

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 the 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.