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

Adeline Augier; Francois Dubois; Benjamin Graille

ESAIM: Proceedings (2012)

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

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topAugier, 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 - Augier, Adeline

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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