Cascaded Lattice Boltzmann Method for Phase-Field Modeling of Incompressible Multiphase Flows*

Two-phase fluid flows with surface tension effects are ubiquitous and challenging due to the simultaneous capturing of interfacial motion and computation of fluid motion at various scales. In this work, we have developed a cascaded lattice Boltzmann (LB) scheme using central moments and multiple relaxation times to represent the advection of an order parameter modeling the dynamics of diffuse interfaces based on a phase field model. The use of central moments improves Galilean invariance and numerical stability. In addition, to handle two-phase flows with large density contrasts in a kinetic formulation, a transformation to the distribution functions needs to be applied in the LB method that reduces the associated stiffness issues. This is accounted for by devising another new cascaded LB scheme for the fluid motion, where the central moment equilibria at different orders are reformulated in terms of the pressure field. Furthermore, the phase segregation and surface tension effects are modeled via forcing terms given in terms of changes in different central moments in this additional cascaded LB flow solver that computes the pressure and the velocity fields. Simulations of a variety of two-phase flow benchmark problems validate the new approach.