Tutorial: Multi-Species Lattice Boltzmann Models and Applications

Kinetic theory of rarefied gas mixtures
Full Boltzmann equations
Full Boltzmann equations for gas mixtures
The simultaneous Boltzmann equations for a mixture without
external force can be written as [3, 4, 5, 6]:
∂ t f σ + ξ·∇f σ + a σ ·∇ ξ f σ = Q σ = ∑ ς
Q σς , (1)
where Q σς = Q ςσ , ς ≠ σ, is the cross collision term for two
different species σ (with mass m σ ) and ς (with mass m ς ).
Obviously, for an N-component system, there will be N such
equations. In general, the collision term is
∫ ∫
Q σς ˙= K σς (g, n) [ f σ (ξ ′ )f ς (ξ ∗) ′ − f σ (ξ)f ς (ξ ∗ ) ] dn dξ ∗ ,
R 3 ξ
g·n