Multiple-relaxation-time lattice Boltzmann scheme for homogeneous mixture flows with external force

A lattice Boltzmann scheme is developed for homogeneous mixture modeling, based on the multiple-relaxation-time (MRT) formulation, which fully recovers the Maxwell-Stefan diffusion model in the continuum limit with (a) external force and (b) tunable Schmidt number. The theoretical basis of the proposed MRT formulation is a recently proposed Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [Andries et al., J. Stat. Phys. 106, 993 (2002)] and it substantially extends the applicability of a scheme already proposed by the same author, which used only one relaxation parameter. The recovered equations at the macroscopic level are derived by an innovative expansion technique, based on the Grad moment system. Some numerical simulations are reported for the solvent test case with external force, aiming to find the numerical ranges for the transport coefficients that ensure acceptable accuracies. The numerical results reduce the theoretical expectations, which are based on a strong separation among the characteristic scales.