  This paper reports the investigations done to adapt the Characteristic
Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds
number applications. Three CBC formalisms are implemented and tested in an open
source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach,
its extension including the effects of the transverse terms (CBC-2D) and a
local streamline approach in which the problem is reformulated in the incident
wave framework (LS-LODI). Then all implementations of the CBC methods are
tested for a variety of test cases, ranging from canonical problems (such as 2D
plane and spherical waves and 2D vortices) to a 2D NACA profile at high
Reynolds number ($Re = 10^5$), representative of aeronautic applications. The
LS-LODI approach provides the best results for pure acoustics waves (plane and
spherical waves). However, it is not well suited to the outflow of a convected
vortex for which the CBC-2D associated with a relaxation on density and
transverse waves provides the best results. As regards numerical stability, a
regularized adaptation is necessary to simulate high Reynolds number flows. The
so-called regularized FD (Finite Difference) adaptation, a modified regularized
approach where the off-equilibrium part of the stress tensor is computed thanks
to a finite difference scheme, is the only tested adaptation that can handle
the high Reynolds computation.
