  The work of Ansumali \textit{et al.}\cite{Ansumali} is extended to Two
Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to
small spatial scales and thus requires subgrid modeling. Applying large eddy
simulation (LES) modeling of the macroscopic fluid equations results in the
need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic
lattice Boltzmann representation from which one can recover the MHD equations
in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen
limit). Thus on first performing filter width expansions on the lattice
Boltzmann equations followed by the standard small Knudsen expansion on the
filtered lattice Boltzmann system results in a closed set of MHD turbulence
equations provided we enforce the physical constraint that the subgrid effects
first enter the dynamics at the transport time scales. In particular, a
multi-time relaxation collision operator is considered for the density
distribution function and a single relaxation collision operator for the vector
magnetic distribution function. The LES does not destroy the property that
$\nabla \cdot \mathbf B = 0$ automatically without the need for divergence
cleaning.
