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.
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