A multispecies, multispeed lattice Boltzmann model is presented to study the mass diffusion properties. At each node the total momentum of all particles and the partial masses of the particles of same species are conserved. Using the Chapman-Enskog method, we have derived from the BGK Boltzmann equation the N-S equation and partial mass conservation equations. We have compared the measured diffusivities with the theoretical values for different single relaxation time, showing good agreemellt. We have carried out the 2-D convection-diffusion simulations on a 16o × 100 hexagonal lattice. At the initial time we inject a bubble of radius r(= l6 nodes), at rest, filled with particles of one species into a uniform flow of particles of the other species. The mean velocity v = 0.5 is along the horizontal axis. One clearly observes the deformation and the diffusion of the bubble.
The Lyapunov method is applied to finite difference equations in order to study the stability and asymptotic properties of Boltzmann equation of lattice gas. The existence and uniqueness of the equilibrium state are proved. A Lyapunov function can be formed by means of function H that is decreasing and takes its minimum value at the equilibrium state. By the Lyapunov function the stability is Obtained. Moreover, a sufficient condition is provided that makes the function H strictly decrease except at the equilibrium state. The asymptotic stability for homogeneous Boltzmann equation of lattice gas is proved under this condition.
