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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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Lattice Relaxation Schemes

Lattice Relaxation Schemes

(p.223) 14 Lattice Relaxation Schemes
The Lattice Boltzmann Equation

Sauro Succi

Oxford University Press

In Chapter 13, it was shown that the complexity of the LBE collision operator can be cut down dramatically by formulating discrete versions with prescribed local equilibria. In this chapter, the process is taken one step further by presenting a minimal formulation whereby the collision matrix is reduced to the identity, upfronted by a single relaxation parameter, fixing the viscosity of the lattice fluid. The idea is patterned after the celebrated Bhatnagar–Gross–Krook (BGK) model Boltzmann introduced in continuum kinetic theory as early as 1954. The second part of the chapter describes the comeback of the early LBE in optimized multi-relaxation form, as well as few recent variants hereof.

Keywords:   single-relaxation time, multi-relaxation time, Bhatnagar–Gross–Krook model, optimized collisions

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