  NGC 4945 is a Seyfert 2 galaxy at a distance of 3.82 Mpc. Its relative
proximity has permitted a detailed SMA study of the circumnuclear molecular gas
in a galaxy exhibiting an AGN. Based on an analysis of the high-resolution
velocity field of the central region (20" X 20", 1" = 19 pc), we demonstrate
that the S-shaped structure of the isovelocity contours is well reproduced by
the numerical results of a two dimensional hydrodynamical simulation. In
particular, the velocity structure is represented by the bending produced by a
shock along the spiral density waves, which are excited at the outer-inner
Lindblad resonance by a fast rotating bar. The simulated density map reveals a
pair of tightly wound spirals in the center which pass through most of the
ring-like (claimed to be a circumnuclear starburst ring by other authors) high
intensity region in the observations as well as intersect several Pa$\alpha$
emission line knots located outside the ring-like region. The calculated mass
inflow rate at a scale of 50 pc is about three times the inferred mass
accretion rate of the AGN of NGC 4945. We find that self-gravity of the gas is
important and should be included in our model for NGC 4945. The model is
compared with the gas orbit model discussed in Lim et al. (2009), and it is
shown that the hydrodynamic model provides a better match to the observed
position-velocity diagram and, hence, provides a more reliable prediction of
the outer inner Lindblad resonance position.
