A consistent lattice Boltzmann equation with baroclinic coupling for mixtures

We propose a consistent lattice Boltzmann equation (LBE) with baroclinic coupling between species and mixture dynamics to model the active scalar dynamics in multi-species mixtures. The proposed LBE model is directly derived from the linearized Boltzmann equations for mixtures and it has the following two distinctive features. First, it uses the multiple-relaxation-time collision model so that it has the flexibility of independent Reynolds and Schmidt numbers, and better numerical stability. Second, it satisfies the indifferentiability principle therefore leads to a set of consistent hydrodynamic equations for barycentric velocity for mixtures. The proposed LBE model is validated through simulations of decaying homogeneous isotropic turbulence in three dimensions. We simulate both the active and passive scalar dynamics in decaying turbulence for mixtures. We also compute various statistical quantities and their decay exponents in decaying turbulence. Our results agree well with existing results for both scalar dynamics and decaying turbulence.