Three-dimensional multi-relaxation time lattice-Boltzmann model for the drop impact on a dry surface at large density ratio

Extensive application of the multiphase lattice Boltzmann model to realistic fluid flows is often restricted by the numerical instabilities induced at high liquid-to-gas density ratios, and at low viscosities. In this paper, a three-dimensional multi-relaxation time (MRT) lattice Boltzmann model with an improved forcing scheme is reported for simulating multiphase flows at high liquid-to-gas density ratios and relatively high Reynolds numbers. The model is based on a recently presented model in the literature. Firstly, the MRT multiphase model is evaluated by verifying Laplace's law and achieving thermodynamic consistency for a static droplet. Then, a relationship between the fluid-solid interaction potential parameter and contact angle is investigated. Finally, the improved three-dimensional MRT Lattice Boltzmann model is employed in the simulation of the impingement of a liquid droplet onto a flat surface for a range of Weber and Reynolds numbers. The dynamics of the droplet spreading is reproduced and the predicted maximum spread factor is in good agreement with experimental data published in the literature.