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

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.