We first recall our analysis of the bounce-back boundary condition based on an asymptotic singular expansion as the mesh size tends to zero. Then it is natural to extend the previous work at first order and a natural extension of the previous analysis is straightforward. As a consequence, we propose a boundary condition able to capture exactly quadratic velocity profiles without any need of "quartic" relaxation parameters.

Prof. Francois Dubois got his PHD degree from University Paris 6 in 1988 and finished the Habilitation to conduct researches in University Paris 6 in 1992. He's been University professor of Conservatoire National des Arts et Metiers since 1994 and  Professor of Mathematics Laboratory, "Analyse Numerique et Equations aux Derivees Particelles", University Paris-Sud since 2003. His main research interests are on mathematical and numerical modelling, quantum modelling, lattice Boltzmann schemes, discrete topology, finite volumes, hyperbolic problems.