A novel one-step simplified lattice Boltzmann method and its application to multiphase flows with large density ratio

Abstract

Recently, a one-step simplified lattice Boltzmann method abandoning the original predictor–corrector scheme has been proposed for single-phase flows. In this method, the information of non-equilibrium distribution function (DF) is implicitly included in the difference of two equilibrium DFs at two different locations and time levels. Due to this treatment, the one-step method faces challenges such as extra virtual memory cost and additional boundary treatments. To overcome these drawbacks, a novel one-step simplified lattice Boltzmann method (NOSLBM) is developed by directly constructing the non-equilibrium DF with macroscopic variables. The NOSLBM preserves the merits of high computational efficiency and simple code programming in the original one-step method. Moreover, the present method is extended to multiphase flows. One NOSLBM for the solution of the Cahn–Hilliard equation is employed to capture the interface. Another one is adopted to solve the Navier–Stokes equations for the hydrodynamic fields. Numerical tests about interface capturing and single-phase flows indicate that the present method has a better performance on computational efficiency than that of the simplified multiphase lattice Boltzmann method (SMLBM), in which the predictor–corrector scheme is applied. Numerical tests about binary fluids with large density ratio imply the great accuracy and numerical stability of the present method.