Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model

The lattice Boltzmann method is applied to the study of immiscible two-phase flows using a Rothman-Keller-type (RK) model. The focus is on the algorithm proposed by Latva-Kokko and Rothman, which has been modified and integrated into the Reis and Phillips model, which belongs to the RK family. A key element of the RK model is the recoloring step applied at the interface of two fluids, at which the fluids are separated and sent to their own region. When convection is weak, the interface in the Reis and Phillips model suffers from “lattice pinning”, which is a problem that may prevent the interface from moving. While the recoloring algorithm proposed by Latva-Kokko and Rothman diminishes this problem, it was not used in the work of Reis and Phillips. This is the framework in which the present study has been conducted. Its scope is twofold: first, to integrate and adapt the Latva-Kokko and Rothman recoloring algorithms for reducing the lattice pinning problem found in the Reis and Phillips model; and second, to conduct a set of numerical tests to show that the combination of the two algorithms leads to an improvement in the quality of the results, along with a better convergence. The context of the work is two-dimensional, with the D2Q9 lattice used as the basic computational element.