Lattice Boltzmann Framework for Multiphase Flows by Eulerian–Eulerian Navier–Stokes Equations

Although the lattice Boltzmann method (LBM) is relatively straightforward, it demands a well-crafted framework to handle the complex partial differential equations involved in multiphase flow simulations. For the first time to our knowledge, this work proposes a novel LBM framework to solve Eulerian–Eulerian multiphase flow equations without any finite difference correction, including very-large-density ratios and also a realistic relation for the drag coefficient. The proposed methodology and all reported LBM formulas can be applied to any dimension. This opens a promising venue for simulating multiphase flows in large High Performance Computing (HPC) facilities and on novel parallel hardware. This LBM framework consists of six coupled LBM schemes—running on the same lattice—ensuring an efficient implementation in large codes with minimum effort. The preliminary numeral results agree in an excellent way with the reference numerical solution obtained by a traditional finite difference solver.