Lattice Boltzmann framework for multiphase flows by Eulerian-Eulerian Navier-Stokes equations

Although 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 on 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 a reference numerical solution obtained by a traditional finite difference solver.