Tutorial: Multi-Species Lattice Boltzmann Models and Applications
Tutorial: Multi-Species Lattice Boltzmann Models and Applications
Tutorial: Multi-Species Lattice Boltzmann Models and Applications
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Lattice</strong> <strong>Boltzmann</strong> solvers <strong>and</strong> applications<br />
LBM formulation by variable transformation<br />
Solution: solving locally a linear system of equations<br />
In the general case, Eq. (45) can be recasted as<br />
〈V i g σ + 〉 = q<br />
σi + − θ ∑<br />
λ+ σ χ σς (x + σ q<br />
ςi + − x+ ς q<br />
σi + ), (46)<br />
ς<br />
where q<br />
σi + = ρ+ σ u + σi <strong>and</strong> χ σς =<br />
m2 B σς<br />
. (47)<br />
m σ m ς B mm<br />
Finally, grouping together common terms yields<br />
[<br />
]<br />
∑<br />
〈V i g σ + 〉 = 1 + θ λ + σ (χ σς x + ς ) q<br />
σi + − θ λ+ σ x + σ<br />
ς<br />
∑<br />
(χ σς q<br />
ςi + ). (48)<br />
ς<br />
Clearly the previous expression defines a linear system of<br />
algebraic equations for the unknowns q + σi .<br />
Pietro Asinari, PhD (Politecnico di Torino) <strong>Multi</strong>-<strong>Species</strong> LB <strong>Models</strong> Rome, Italy, on July 5-9, 2010 28 / 51
Change language