  We show that the asymptotic properties of the link-wise artificial
compressibility method are not compatible with a correct approximation of fluid
properties. We propose to adapt the previous method through a framework
suggested by the Taylor expansion method and to replace first order terms in
the expansion by appropriate three or five points finite differences and to add
non linear terms. The "FD-LBM" scheme obtained by this method is tested in two
dimensions for shear wave, Stokes modes and Poiseuille flow. The results are
compared with the usual lattice Boltzmann method in the framework of multiple
relaxation times.
