An improved hydrodynamics formulation for multiphase flow lattice-Boltzmann models

Lattice-Boltzmann (LB) models provide a systematic formulation of effective -field computational approaches to the calculation of multiphase flow by re placing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuo usly. Many existing multiphase models of this sort do not satisfy the rigor ous hydrodynamic constitutive laws. Here, we extend the two-dimensional, se ven-speed Swift et al. LB model(1) to rectangular grids (nine speeds) by us ing symbolic manipulation (Mathematica(TM)) and compare the LB model predic tions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the tw o-phase analogue of the Couette flow and with a flow involving shear and ad vection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to sa tisfy the Navier-Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formu lation.