A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach Original Research Article

A Galilean invariant model of the lattice Boltzmann method (LBM) for multiphase fluid flows using free-energy approach is proposed. The asymptotic theory proposed by Sone (1971) is applied to the LBM model for multiphase fluid flows using the free-energy approach developed by Swift et al. [Phys. Rev. Lett. 75 (1995) 830] and governing equations for macroscopic variables of the model are obtained. From the governing equations the condition of a Galilean invariant LBM model is identified. In two problems, moving droplet and drop deformation and breakup in a shear flow, Galilean invariance of the proposed model is demonstrated.