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The Lattice Boltzmann EquationFor Complex States of Flowing Matter$
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Sauro Succi

Print publication date: 2018

Print ISBN-13: 9780199592357

Published to Oxford Scholarship Online: June 2018

DOI: 10.1093/oso/9780199592357.001.0001

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From Kinetic Theory to Navier–Stokes Hydrodynamics

From Kinetic Theory to Navier–Stokes Hydrodynamics

(p.70) 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
The Lattice Boltzmann Equation

Sauro Succi

Oxford University Press

This Chapter illustrates the derivation of the macroscopic fluid equations, starting from Boltzmann’s kinetic theory. Two routes are presented, the heuristic derivation based on the enslaving of fast modes to slow ones, and the Hilbert–Chapman–Enskog procedure, based on low-Knudsen number asymptotic expansions. The former is handier but mathematically less rigorous than the latter. Either ways, the assumption of weak departure from local equilibrium proves crucial in recovering hydrodynamics as a large-scale limit of kinetic theory.

Keywords:   fluid dynamic limit, Knudsen number, Hilbert expansion, Chapman-Enskog expansion, enslaving principle

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