On a superconvergent lattice Boltzmann boundary scheme

François Dubois (1, 2) , Pierre Lallemand (3) , Mohamed Mahdi Tekitek (2)

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

In a seminal paper Ginzburg and Adler analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the Poiseuille flow if some expressions depending upon the parameters of the method were satisfied, thus defining so-called "magic parameters". Using the Taylor expansion method that one of us developed, we analyze a series of simple situations (1D and 2D) for diffusion and for linear fluid problems using bounce-back and "anti bounce-back" numerical boundary conditions. The result is that "magic parameters" depend upon the detailed choice of the moments and of their equilibrium values. They may also depend upon the way the flow is driven.

Mots clés: Lattice Boltzmann scheme; boundary conditions; Taylor expansion method

Domaines: Analyse numérique [math.NA]

François Dubois, Pierre Lallemand, Mohamed Mahdi Tekitek. On a superconvergent lattice Boltzmann boundary scheme. Computers & Mathematics with Applications, 2010, 59 (7), pp.2141-2149. ⟨10.1016/j.camwa.2009.08.055⟩. ⟨hal-00986823⟩