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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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The Hermite–Gauss Route to LBE

The Hermite–Gauss Route to LBE

Chapter:
(p.237) 15 The Hermite–Gauss Route to LBE
Source:
The Lattice Boltzmann Equation
Author(s):

Sauro Succi

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199592357.003.0015

This chapter describes the side-up approach to Lattice Boltzmann, namely the formal derivation from the continuum Boltzmann-(BGK) equation via Hermite projection and subsequent evaluation of the kinetic moments via Gauss–Hermite quadrature. From a slightly different angle, one may also interpret the Gauss–Hermite quadrature as an optimal sampling of velocity space, or, better still, an exact sampling of the bulk of the distribution function, the one contributing most to the lowest order kinetic moments (frequent events). Capturing higher–order moments, beyond hydrodynamics (rare events), requires an increasing number of nodes and weights.

Keywords:   Gauss–Hermite quadrature, kinetic moments, projection methods, side-up approach

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