  We present smoothed particle hydrodynamic models of the interactions in the
compact galaxy group, Stephan's Quintet. This work is extension of the earlier
collisionless N-body simulations of Renaud et al. in which the large-scale
stellar morphology of the group was modeled with a series of galaxy-galaxy
interactions in the simulations. Including thermohydrodynamic effects in this
work, we further investigate the dynamical interaction history and evolution of
the intergalactic gas of Stephan's Quintet. The major features of the group,
such as the extended tidal features and the group-wide shock, enabled us to
constrain the models reasonably well, while trying to reproduce multiple
features of the system. We found that reconstructing the two long tails
extending from NGC 7319 toward NGC 7320c one after the other in two separate
encounters is very difficult and unlikely, because the second encounter usually
destroys or distorts the already-generated tidal structure. Our models suggest
the two long tails may be formed simultaneously from a single encounter between
NGC 7319 and 7320c, resulting in a thinner and denser inner tail than the outer
one. The tails then also run parallel to each other as observed. The model
results support the ideas that the group-wide shock detected in
multi-wavelength observations between NGC 7319 and 7318b and the starburst
region north of NGC 7318b are triggered by the high-speed collision between NGC
7318b and the intergalactic gas. Our models show that a gas bridge is formed by
the high-speed collision and clouds in the bridge continue to interact for some
tens of millions of years after the impact. This produces many small shocks in
that region, resulting a much longer cooling time than that of a single impact
shock.
