On rotational invariance of lattice Boltzmann schemes

Adeline Augier (1) , François Dubois (1, 2) , Benjamin Graille (1) , Pierre Lallemand (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
3 CSRC - Beijing Computational Science Research Center [Beijing]

We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding linear equivalent partial differential equations are generated with a new ''Berliner version'' of the Taylor expansion method. The details of the implementation are presented. These ideas are applied for the D2Q9, D2Q13, D3Q19 and D3Q27 lattice Boltzmann schemes. Some limitations associated with necessary stability conditions are also presented.

Mots clés: Acoustics; Taylor expansion method; linearized Navier-Stokes; isotropy

Domaines: Analyse numérique [math.NA]; Automates cellulaires et gaz sur réseau [nlin.CG]

Adeline Augier, François Dubois, Benjamin Graille, Pierre Lallemand. On rotational invariance of lattice Boltzmann schemes. 2013. ⟨hal-00923240⟩