Volume 35, March 2012Congrès National de Mathématiques Appliquées et Industrielles
|Page(s)||191 - 196|
|Published online||06 April 2012|
Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*
Université Paris Sud, Laboratoire de mathématiques, UMR
e-mail: firstname.lastname@example.org, email@example.com & firstname.lastname@example.org
2 Conservatoire National des Arts et Métiers, Department of mathematics, Paris, France
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.
Key words: lattice Boltzmann schemes / isotropy / formal calculus / Taylor expansion method / equivalent equations
© EDP Sciences, SMAI 2012
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