  In this paper, we investigate the hydrodynamic collectivity in proton--proton
(pp) collisions at 13 TeV, using iEBE-VISHNU hybrid model with HIJING initial
conditions. With properly tuned parameters, our model simulations can
remarkably describe all the measured 2-particle correlations, including
integrated and differential elliptic flow coefficients for all charged and
identified hadrons ($K_S^0$, $\Lambda$). However, our model calculations show
positive 4-particle cumulant $c_{2}\{4\}$ in high multiplicity pp collisions,
and can not reproduce the negative $c_{2}\{4\}$ measured in experiment. Further
investigations on the HIJING initial conditions show that the fluctuations of
the second order anisotropy coefficient $\varepsilon_{2}$ increases with the
increase of its mean value, which leads to a similar trend of the flow
fluctuations. For a simultaneous description of the 2- and 4- particle
cumulants within the hydrodynamic framework, it is required to have significant
improvements on initial condition for pp collisions, which is still lacking of
knowledge at the moment.
