Lattice Boltzmann model approximated with finite difference expressions

François Dubois (1, 2) , Pierre Lallemand (3) , Christian Obrecht (4) , Mohamed Mahdi Tekitek (5)

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]
4 CETHIL - Centre de Thermique de Lyon
5 UTM - Université de Tunis El Manar

We show that the asymptotic properties of the link-wise artificial com-pressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt the previous method through a framework suggested by the Tay-lor expansion method and to replace first order terms in the expansion by appropriate three or five points finite differences and to add non linear terms. The " FD-LBM " scheme obtained by this method is tested in two dimensions for shear wave, Stokes modes and Poiseuille flow. The results are compared with the usual lattice Boltzmann method in the framework of multiple relaxation times.

Mots clés: artificial compressibility method; quartic parameters

Domaines: Analyse numérique [math.NA]; Milieux fluides et réactifs

François Dubois, Pierre Lallemand, Christian Obrecht, Mohamed Mahdi Tekitek. Lattice Boltzmann model approximated with finite difference expressions. Computers and Fluids, 2017, 155, pp.3 - 8. ⟨10.1016/j.compfluid.2016.04.013⟩. ⟨hal-01718120⟩