  We present a new method for the numerical implementation of generating
boundary conditions for a one dimensional Boussinesq system. This method is
based on a reformulation of the equations and a resolution of the dispersive
boundary layer that is created at the boundary when the boundary conditions are
non homogeneous. This method is implemented for a simple first order finite
volume scheme and validated by several numerical simulations. Contrary to the
other techniques that can be found in the literature, our approach does not
cause any increase in computational time with respect to periodic boundary
conditions.
