Geodesic
Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9
Adeline Augier1 ; Francois Dubois1, 2 ; Benjamin Graille1
1Université Paris Sud, Laboratoire de mathématiques, UMR 8628, Orsay, F-91M05, France
2Conservatoire National des Arts et Métiers, Department of mathematics, Paris, France
ESAIM. Proceedings, Tome 35 (2012), pp. 191-196
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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.
DOI : 10.1051/proc/201235013

Adeline Augier  1   ; Francois Dubois  1 , 2   ; Benjamin Graille  1

1 Université Paris Sud, Laboratoire de mathématiques, UMR 8628, Orsay, F-91M05, France
2 Conservatoire National des Arts et Métiers, Department of mathematics, Paris, France 
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     author = {Adeline Augier and Francois Dubois and Benjamin Graille},
     title = {Isotropy conditions for lattice {Boltzmann} schemes. {Application} to {D2Q9}},
     journal = {ESAIM. Proceedings},
     pages = {191--196},
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     doi = {10.1051/proc/201235013},
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Adeline Augier; Francois Dubois; Benjamin Graille. Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9. ESAIM. Proceedings, Tome 35 (2012), pp. 191-196. doi: 10.1051/proc/201235013

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