Tutorial: Multi-Species Lattice Boltzmann Models and Applications
Tutorial: Multi-Species Lattice Boltzmann Models and Applications
Tutorial: Multi-Species Lattice Boltzmann Models and Applications
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<strong>Lattice</strong> <strong>Boltzmann</strong> solvers <strong>and</strong> applications<br />
Andries-Aoki-Perthame (AAP) model<br />
Tuning the single species relaxation frequency<br />
Taking the first order moments of g (1)<br />
σ<br />
where p (k)<br />
σ<br />
= ϕ σ ρ (k)<br />
σ /3.<br />
yields<br />
λ σ ρ (0)<br />
σ [u ∗(1)<br />
σ − u (1)<br />
σ ] = ∇p (0)<br />
σ , (32)<br />
If λ σ is selected as λ σ = p B mm /ρ, then the previous expression<br />
becomes<br />
1/p (0) ∇p (0)<br />
σ<br />
= ∑ ς<br />
B σς y σ y ς [u (1)<br />
ς − u (1)<br />
σ ], (33)<br />
which clearly proves that the leading terms of the macroscopic<br />
equations recovered by means of the AAP model are consistent<br />
with Maxwell-Stefan model.<br />
Pietro Asinari, PhD (Politecnico di Torino) <strong>Multi</strong>-<strong>Species</strong> LB <strong>Models</strong> Rome, Italy, on July 5-9, 2010 19 / 51