A fractional-step lattice Boltzmann method for multiphase flows with complex interfacial behavior and large density contrast

Abstract

In the present study, a robust fractional-step lattice Boltzmann (FSLB) method is proposed to simulate the mass transfer phenomenon in incompressible multiphase flows with complex interfacial behavior and large density contrast. The previous simplified lattice Boltzmann method recovers the continuity equation in first-order accuracy and reconstructs the corrector step by directly applying the complex central difference scheme on the macroscopic variables. However, the present FSLB method employs the Chapman-Enskog expansion analysis to reconstruct the convection and diffusion terms of the macroscopic governing equations, and uses the equilibrium and non-equilibrium distribution functions to establish the predictor-corrector step. The intermediate variables are predicted by the equilibrium distribution functions without the consideration of the source terms, and then the physical variables are corrected by the non-equilibrium distribution functions and the source terms without the evolution of the distribution functions. The reconstructed governing equations in both the predictor and corrector steps can be recovered into fully second-order accuracy through the C-E expansion analysis and the Taylor series expansion analysis. The present FSLB method inherits the excellent performance of kinetic theory from the conventional LB method and the good numerical stability from the matured fractional-step method, which is validated by several benchmark problems, such as Laplace law, bubble merging, interfacial deformation under a magnetic field, Rayleigh-Taylor instability at Reynolds number of 3000, Kelvin-Helmholtz instability at Reynolds number of 5000, and bubble rising at density ratio of 1000. A good agreement between the present numerical results with the published numerical data verifies the capability and reliability of the present FSLB method to handle the multiphase problems with complex interfacial behavior and large density contrast.