Implementation of a Lattice Boltzmann Method for Multiphase Flows with High Density and Viscosity Ratios

Abstract: We present a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. Following Banari et al. (2014), the motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure-less Navies-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test cases. Here, we present results for some complex flow problems including two dimensional single and multiple mode Rayleigh-Taylor Instability (RTI).  Also, we present the evolution of the height of a standing wave for both high and low viscosity and density ratios.