Unsteady immiscible multiphase flow validation of a multiple-relaxation-time lattice Boltzmann method

The lattice Boltzmann modeling of immiscible multiphase flows needs to be further validated, especially when density variation occurs between the different flow phases. From this perspective, the goal of this research is to introduce the multiple-relaxation-time operator into a lattice Boltzmann model in order to improve its numerical stability in the presence of large density and viscosity ratios. Essentially, this research shows that the introduction of this operator greatly improves the numerical stability of the approach compared to the original single-relaxation-time collision operator. In many lattice Boltzmann research studies, multiphase lattice Boltzmann methods are validated using a reduced number of test cases, and unsteady flow test cases are frequently omitted before much more complex flow configurations are simulated. In this context, several test cases are proposed to evaluate the behavior of a lattice Boltzmann method for simulating immiscible multiphase flows with high density and viscosity ratios. These are: (1) two-phase Couette flow; (2) three-phase Laplace law; (3) three-phase Zalesak disk; (4) two-phase flow between oscillating plates; (5) two-phase capillary wave; and (6) the two-phase oscillating cylindrical bubble. The first two involve a steady regime, and the remaining four an unsteady regime.