Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9

Adeline Augier, Francois Dubois, Benjamin Graille
2012 ESAIM: Proceedings and Surveys  
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
more » ... rium 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. * This work has been financially supported by the French Ministry of Industry (DGCIS) and the Region Ile-de-France in the framework of the LaBS Project [1].
doi:10.1051/proc/201235013 fatcat:7qks67hpjfbvfac3qcutidspee