Taylor Expansion Method for Linear Lattice Boltzmann Schemes with an External Force: Application to Boundary Conditions

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

1 LMO - 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 Dep. Math. Faculty of Sciences of Tunis

In this contribution we show that it is possible to get the macroscopic fluid equations of a lattice Boltzmann scheme with an external force using the Taylor expansion method. We validate this general expansion by a detailed analysis of the boundary conditions. We derive ``quartic parameters'' that enforce the precision of the boundary scheme. We explicit and validate the corresponding relations for a Poiseuille flow computed with the D2Q13 lattice Boltzmann scheme.

Mots clés: bounce-back; adiabatic wall; acoustics; Poiseuille flow

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique Numérique [physics.comp-ph]

François Dubois, Pierre Lallemand, Mohamed Mahdi Tekitek. Taylor Expansion Method for Linear Lattice Boltzmann Schemes with an External Force: Application to Boundary Conditions. European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications, HONOM 2013, Mar 2013, Bordeaux, France. pp.89-107, ⟨10.1007/978-3-319-05455-1_6⟩. ⟨hal-00864541v2⟩