  The flow of amorphous solids results from a combination of elastic
deformation and local structural rearrangements, which induce non-local elastic
deformations. These elements are incorporated into a mechanically-consistent
mesoscopic model of interacting elastoplastic blocks. We investigate the
specific case of channel flow with numerical simulations, paying particular
attention to situations of strong confinement. We find that the simple picture
of plastic events embedded in an elastic matrix successfully accounts for
manifestations of spatial cooperativity. Shear rate fluctuations are observed
in seemingly quiescent regions, and the velocity profiles in confined flows at
high applied pressure deviate from those expected in the absence of non-local
effects, in agreement with experimental data. However, we suggest a different
physical origin for the large deviations observed when walls have rough
surfaces, associated with "bumps" of the particles against the asperities of
the walls.
