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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Kinetic theory of rarefied gas mixtures<br />
Full <strong>Boltzmann</strong> equations<br />
Indifferentiability Principle <strong>and</strong> H–theorem<br />
Indifferentiability Principle: when all the masses m σ <strong>and</strong><br />
cross-sections K σς are identical, the total distribution f = ∑ σ f σ<br />
obeys the single species <strong>Boltzmann</strong> equation.<br />
H–theorem: in the case of a mixture, the entropy inequality<br />
(H–theorem) is<br />
∑<br />
∫<br />
Q σ log(f σ )dξ ≤ 0. (6)<br />
σ<br />
R 3 ξ<br />
These properties of the full <strong>Boltzmann</strong> equations for mixtures will<br />
guide the design of BGK–type simplified models <strong>and</strong> consequently<br />
of the <strong>Lattice</strong> <strong>Boltzmann</strong> solvers.<br />
Pietro Asinari, PhD (Politecnico di Torino) <strong>Multi</strong>-<strong>Species</strong> LB <strong>Models</strong> Rome, Italy, on July 5-9, 2010 7 / 51
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