LATTICE BHATNAGAR-GROSS-KROOK MODELS FOR MISCIBLE FLUIDS

Lattice Bhatnagar-Gross-Krook models for miscible fluid flow in two (2 D) and three (3D) dimensions are introduced. The convection-diffusion (CD) equation and the Navier-Stokes (NS) equation describing the macro scopic behavior of the models are derived using the Chapman-Enskog exp ansion technique. Corrections to the CD equation of higher order in th e flow velocity are obtained, and it is shown how the present models a re linked with the existing Boltzmann model. It is also shown how the Navier-Stokes dynamics is explicitly decoupled from the diffusive beha vior of the model. The results obtained from both 2D and 3D simulation s are observed to be in excellent agreement with the analytic predicti ons. In particular it is shown that the models are well described by t heory for high-Peclet-number flows. We also present simulation results confirming the anomalous (but small) velocity dependence of the CD eq uation, and we investigate the models' sensitivity to large gradients in the concentration profile.