I'm implementing a solver leveraging the Lattice Boltzmann method for Basic Oxygen Furnace simulations (using multiple-relaxation time and D3Q27 cell model), where the jet blows oxygen onto slag surface with speeds of 1.5-2.5 Mach. Process involves multiphase flows, phase transitions, combustion, and turbulent behavior of slag fluid around the interface with blown oxygen. My current focus is on the gas-fluid interface and the impact of the high-Mach flow of oxygen.
I would like to ask what would be the best approach for simulating such phenomena with LBM and MRT scheme?