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

Abstract

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 etal. [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 etal. [Phys. Rev. E 94, 023310 (2016)10.1103/PhysRevE.94.023310] and earlier Liu etal. [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 etal., verify the utility of MRT chromodynamic MCLBE.