  The ALICE Collaboration measure the three- and four-pion Bose-Einstein
correlations (BECs) in Pb-Pb collisions at the Large Hadron Collider (LHC). It
is speculated that the significant suppressions of multi-pion BECs are due to a
considerable degree of coherent pion emission in the collisions. In this paper,
we study the multi-pion BEC functions in a granular source model with coherent
pion-emission droplets. We find that the intercepts of multi-pion correlation
functions at the relative momenta near zero are sensitive to droplet number in
the granular source. They decrease with decreasing droplet number. The
three-pion correlation functions for the evolving granular sources with
momentum-dependent partially coherent pion-emission droplets are in basic
agreement with the experimental data in Pb-Pb collisions at
$\sqrt{s_{NN}}=2.76$ TeV at the LHC. However, the model results of four-pion
correlation function are inconsistent with the experimental data. The
investigations of the normalized multi-pion correlation functions of the
granular sources indicate that there is an interesting enhancement of the
normalized four-pion correlation function in moderate relative-momentum region.
