  We investigate two-fluid BGK kinetic methods for binary fluids. The developed
theory works for asymmetric as well as symmetric systems. For symmetric systems
it recovers Sirovich's theory and is summarized in models A and B. For
asymmetric systems it contributes models C, D and E which are especially useful
when the total masses and/or local temperatures of the two components are
greatly different. The kinetic models are discretized based on an octagonal
discrete velocity model. The discrete-velocity kinetic models and the
continuous ones are required to describe the same hydrodynamic equations. The
combination of a discrete-velocity kinetic model and an appropriate
finite-difference scheme composes a finite-difference lattice Boltzmann method.
The validity of the formulated methods is verified by investigating (i) uniform
relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion
behavior.
