Spurious velocity from the cutoff and magnification equation in free energy-based LBM for two-phase flow with a large density ratio

Abstract

The spurious velocity resulting from the cutoff and magnification equation in the free-energy-based one-component-two-phase flow lattice Boltzmann method (LBM) for a large density ratio proposed by Inamuro et al. [34] is investigated. In Inamuro’s model, the phase interface is tracked by the order parameter, which is the dimensionless density of a two-phase flow system with a small density ratio. The velocity field is calculated based on the density profile of a two-phase system with a large density ratio, which is derived from the order parameter profile through a sine type of cutoff and magnification equation; this velocity field is then used to drive the movement of a phase interface described by the order parameter. The implementation of the cutoff and magnification equation causes the density profiles in the two systems to differ from each other such that force balances across the interfaces break from the ideal state and lead to spurious velocity. Three measures: (1) the linear cutoff and magnification equation which equalizes the density profiles in the interface region, (2) a new scheme which enhances the smoothness of the density profile around the cutoff points in the large density ratio system and (3) a special method that increases the interface thickness of the large density ratio system are adopted to reduce the magnitude of the spurious velocity from the profile difference, respectively. We show that all of these measures can successfully reduce the magnitude of the spurious velocity to some degree; and the scheme that enhances the smoothness of the density profile around the cutoff points reduces the spurious velocity of the original scheme by one order of magnitude.