Tutorial: Multi-Species Lattice Boltzmann Models and Applications

Lattice Boltzmann solvers and applications
Rule of computation for the list
LBM formulation by variable transformation
The components of the molecular velocity V 1 and V 2 are the lists
with 9 elements. Before proceeding to the definition of the local
equilibrium function f σ(∗) , we define the rule of computation for the
list.
Let h and g be the lists defined by h = [h 0 , h 1 , h 2 , · · · , h 8 ] T and
g = [g 0 , g 1 , g 2 , · · · , g 8 ] T . Then, hg is the list defined by
[h 0 g 0 , h 1 g 1 , h 2 g 2 , · · · , h 8 g 8 ] T . The sum of all the elements of the list
h is denoted by 〈h〉, i.e. 〈h〉 = ∑ 8
i=0 h i.
Then, the (dimensionless) density ρ σ and momentum q σi = ρ σ u σi
are defined by
ρ σ = 〈f σ 〉, q σi = 〈V i f σ 〉. (37)
Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 21 / 51