Tutorial: Multi-Species Lattice Boltzmann Models and Applications

Lattice Boltzmann solvers and applications
Properties of simplified AAP model
Andries-Aoki-Perthame (AAP) model
The target velocity can be easily recasted as
u ∗ σ = u + ∑ ( )
m
2
B σς
− 1 x ς (u ς − u σ ). (19)
m
ς σ m ς B mm
If m σ = m for any σ, then (Property 1)
u ∗ σ = u + ∑ ς
( m
2
mm
)
B mm
− 1 x ς (u ς − u σ ) = u. (20)
B mm
Clearly (Property 2)
∑
x σ u ∗ σ = u + ∑ σ
σ
∑
( m
2
ς
m σ m ς
)
B σς
− 1 x σ x ς (u ς − u σ ) = u.
B mm
(21)
Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 15 / 51