We have performed smoothed particle hydrodynamics (SPH) simulations for the response of the gaseous disk to the imposed moderately strong non-axisymmetric potentials. The model galaxies are composed of the three stellar components (disk, bulge and bar) and two dark ones (supermassive black hole and halo) whose gravitational potentials are assumed to be invariant in time in the frame corotating with the bar. We found that the torques alone generated by the moderately strong bar that gives the maximum of tangential-to-radial force ratio as $(F_{Tan}/F_{Rad})_{max}= 0.3$ are not sufficient to drive the gas particles close to the center due to the barrier imposed by the inner Lindblad resonances (ILRs). In order to transport the gas particles towards the nucleus ($r<100$ pc), a central supermassive black hole (SMBH) and high sound speed of the gas are required to be present. The former is required to remove the inner inner Lindblad resonance (IILR) that prevents gas inflow close to the nucleus, while the latter provides favourable conditions for the gas particles to lose their angular momentum and to spiral in. Our models that have no IILR show the trailing nuclear spirals whose innermost parts reach close to the center in a curling way when the gas sound speed is $ c_{s} \gtrsim 15$ km s$^{-1}$. They resemble the symmetric two-armed nuclear spirals observed in the central kiloparsec of spiral galaxies. We found that the symmetric two-armed nuclear spirals are formed by the hydrodynamic spiral shocks caused by the gravitational torque of the bar in the presence of a central SMBH that can remove IILR when the sound speed of gas is high enough to drive a large amount of gas inflow deep inside the ILR. However, the detailed morphology of nuclear spirals depends on the sound speed of gas.

38 pages, 10 figures, accepted for publication in ApJ