Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference

We develop, after Dellar [Phys. Rev. E. 65, 036309 (2002)10.1103/PhysRevE.65.036309; J. Comput. Phys. 190, 351 (2003)10.1016/S0021-9991(03)00279-1], a multiple-relaxation-time (MRT), chromodynamic, multicomponent lattice Boltzmann equation (MCLBE) scheme for simulation of isothermal, immiscible fluid flow with a density contrast. It is based on Lishchuk's method [Brackbill, Kothe, and Zemach, J. Comp. Phys. 100, 335 (1992)10.1016/0021-9991(92)90240-Y; Lishchuk, Care, and Halliday, Phys. Rev. E. 67, 036701, (2003)10.1103/PhysRevE.76.036701] and the segregation of d'Ortona et al. [Phys. Rev. E. 51, 3718, (1995)10.1103/PhysRevE.51.3718]. We focus on fundamental model verifiability but do relate some of our data to that from previous approaches, due to Ba et al. [Phys. Rev. E 94, 023310 (2016)10.1103/PhysRevE.94.023310] and earlier Liu et al. [Phys. Rev. E 85, 046309 (2012)10.1103/PhysRevE.85.046309], who pioneered large density difference chromodynamic MCLBE and showed the practical benefits of an MRT collision model. Specifically, we test the extent to which chromodynamic MCLBE MRT schemes comply with the kinematic condition of mutual impenetrability and the continuous traction condition by developing analytical benchmarking flows. We conclude that our data, taken with those of Ba et al., verify the utility of MRT chromodynamic MCLBE.