  In a previous work, we have proposed a method for the analysis of the bounce
back boundary condition with the Taylor expansion method in the linear case. In
this work two new schemes of modified bounce back are proposed. The first one
is based on the expansion of the iteration of the internal scheme of the
lattice Boltzmann method. The analysis puts in evidence some defects and a
generalized version is proposed with a set of essentially four possible
parameters to adjust. We propose to reduce this number to two with the
elimination of spurious density first order terms. Thus a new scheme for bounce
back is found exact up to second order and allows an accurate simulation of the
Poiseuille flow for a specific combination of the relaxation and boundary
coefficients. We have validated the general expansion of the value in the first
cell in terms of given values on the boundary for a stationary "accordion" test
case.
