  In this contribution, we recall the derivation of the anti bounce back
boundary condition for the D2Q9 lattice Boltzmann scheme. We recall various
elements of the state of the art for anti bounce back applied to linear heat
and acoustics equations and in particular the possibility to take into account
curved boundaries. We present an asymptotic analysis that allows an expansion
of all the fields in the boundary cells. This analysis based on the Taylor
expansion method confirms the well known behaviour of anti bounce back boundary
for the heat equation. The analysis puts also in evidence a hidden differential
boundary condition in the case of linear acoustics. Indeed, we observe
discrepancies in the first layers near the boundary. To reduce these
discrepancies, we propose a new boundary condition mixing bounce back for the
oblique links and anti bounce back for the normal link. This boundary condition
is able to enforce both pressure and tangential velocity on the boundary.
Numerical tests for the Poiseuille flow illustrate our theoretical analysis and
show improvements in the quality of the flow.
