# Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*

ESAIM: Proceedings (2012)

• Volume: 35, page 191-196
• ISSN: 1270-900X

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## Abstract

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In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on relaxation times and equilibrium states that characterizes a lattice Boltzmann scheme. We propose a method to select the parameters of the scheme according to the desired order of isotropy. Applying it to the D2Q9 scheme yields the classical constraints for the first and second orders and some non classical for the third and fourth orders.

## How to cite

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Augier, Adeline, Dubois, Francois, and Graille, Benjamin. Denis Poisson, Fédération, and Trélat, E., eds. " Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*." ESAIM: Proceedings 35 (2012): 191-196. <http://eudml.org/doc/251251>.

@article{Augier2012,
abstract = {In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on relaxation times and equilibrium states that characterizes a lattice Boltzmann scheme. We propose a method to select the parameters of the scheme according to the desired order of isotropy. Applying it to the D2Q9 scheme yields the classical constraints for the first and second orders and some non classical for the third and fourth orders.},
author = {Augier, Adeline, Dubois, Francois, Graille, Benjamin},
editor = {Denis Poisson, Fédération, Trélat, E.},
journal = {ESAIM: Proceedings},
keywords = {lattice Boltzmann schemes; isotropy; formal calculus; Taylor expansion method; equivalent equations},
language = {eng},
month = {4},
pages = {191-196},
publisher = {EDP Sciences},
title = { Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*},
url = {http://eudml.org/doc/251251},
volume = {35},
year = {2012},
}

TY - JOUR
AU - Dubois, Francois
AU - Graille, Benjamin
AU - Denis Poisson, Fédération
AU - Trélat, E.
TI - Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*
JO - ESAIM: Proceedings
DA - 2012/4//
PB - EDP Sciences
VL - 35
SP - 191
EP - 196
AB - In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on relaxation times and equilibrium states that characterizes a lattice Boltzmann scheme. We propose a method to select the parameters of the scheme according to the desired order of isotropy. Applying it to the D2Q9 scheme yields the classical constraints for the first and second orders and some non classical for the third and fourth orders.
LA - eng
KW - lattice Boltzmann schemes; isotropy; formal calculus; Taylor expansion method; equivalent equations
UR - http://eudml.org/doc/251251
ER -

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