Progress in Computational Fluid Dynamics, Vol. 8, Nos. 1–4, 2008 49 On numerical reflected waves in lattice Boltzmann schemes M.M. Tekitek Laboratoire de Mathématiques, Université Paris Sud, Bat. 425, 91405 Orsay Cedex, France E-mail: Mohamed-Mahdi.Tekitek@math.u-psud.fr M. Bouzidi Université Clermont 2, I.U.T., Ave. A. Briand 03107, Montluçon Cedex, France E-mail: Bouzidi@asci.fr F. Dubois * CNAM, 292, rue Saint-Martin, 75141 Paris, France E-mail: Francois.Dubois@math.u-psud.fr *Corresponding author P. Lallemand Laboratoire ASCI, Université Paris Sud, Bâtiment 506, 91405 Orsay Cedex, France E-mail: lalleman@asci.fr Abstract: In this contribution, we study the transmission of a one dimensional acoustic wave between two fluid media with the classical lattice Boltzmann scheme. The two media have the same hydrodynamic equations but different equilibrium distributions. We take here the case where the incident wave is normal to the interface. The theoretical modal study of this problem shows the presence of a reflected wave and Knudsen modes localised at the interface. This analysis leads to results in good agreement with numerical simulations. Keywords: lattice Boltzmann; acoustic propagation; acoustic reflection. Reference to this paper should be made as follows: Tekitek, M.M., Bouzidi, M., Dubois, F. and Lallemand, P. (2008) ‘On numerical reflected waves in lattice Boltzmann schemes’, Progress in Computational Fluid Dynamics, Vol. 8, Nos. 1–4, pp.49–55. Biographical notes: Mohamed Mahdi Tekitek is PhD in Applied Mathematics from Paris-Sud University, December 2007. M. Bouzidi is an Assistant Professor at Clermont 2 University, France. François Dubois is Professor of Applied Mathematics at the Conservatoire National des Arts et Métiers, Paris, France. He is member of the Département de Mathématiques of Université Paris-Sud, Orsay, France. Pierre Lallemand is retired and a former research fellow at Centre National de la Recherche Scientifique. Copyright © 2008 Inderscience Enterprises Ltd.