Eliminating spurious currents in phase-field-theory-based lattice Boltzmann equation for two-phase flows

Abstract

Spurious currents are frequently observed near an interface in the equilibrium multiphase flow system by lattice Boltzmann equation (LBE). These unphysical phenomena are the result of force imbalance of LBE at a discrete level. In this paper, we develop a well-balanced Cahn–Hilliard equation-based LBE for incompressible two-phase flows. The effects of small initial perturbation of order parameter or dynamic pressure and nonisotropic discretization of gradient in force term on eliminating the spurious currents are investigated systematically. Numerical simulations including flat interface and stationary droplet problems are carried out to show the capability of present LBE for eliminating the spurious currents and its accuracy. The results predicted by the present LBE are compared with those by mixed isotropic discretizations scheme (MIDS) frequently used in the LBE community. Numerical results show that the initial perturbation of order parameter or dynamic pressure and nonisotropic discretization of gradient term has no significant effect on eliminating the spurious currents by present LBE, while the MIDS is sensitive to them.