Towards higher order lattice Boltzmann schemes

François Dubois (1, 2) , Pierre Lallemand (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
3 Retired from Centre National de la Recherche Scientifique

In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the associated dynamical equations for classical thermal and linear fluid models in one to three space dimensions. We use this approach to adjust relaxation parameters in order to enforce fourth order accuracy for thermal model and diffusive relaxation modes of the Stokes problem. We apply the resulting scheme for numerical computation of associated eigenmodes and compare our results with analytical references.

Mots clés: lattice Boltzmann; Taylor formula; thermics; acoustics; linearized Navier--Stokes; formal calculus

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

François Dubois, Pierre Lallemand. Towards higher order lattice Boltzmann schemes. Journal of Statistical Mechanics: Theory and Experiment, 2009, 2009 (P06), pp.P06006. ⟨10.1088/1742-5468/2009/06/P06006⟩. ⟨hal-00336388v3⟩