Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics
  We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic properties such as shear-thinning and shear-banding. 
Colin Denniston, Enzo Orlandini, and J.M. Yeomans