We present one-dimensional numerical simulations, which consider the effects of radiative cooling and gravity on the hydrodynamics of the matter reinserted by stellar winds and supernovae within young nuclear starbursts (NSBs) with a central supermassive black hole (SMBH). The simulations confirm our previous semi-analytic results for lowenergetic starbursts, evolving in a quasi-adiabatic regime, and extend them to more powerful starbursts evolving in the catastrophic cooling regime. The simulations show a bimodal hydrodynamic solution in all cases. They present a quasi-stationary accretion flow onto the black hole, defined by the matter reinserted by massive stars within the stagnation volume and a stationary starburst wind, driven by the high thermal pressure acquired in the region between the stagnation and the starburst radii. In the catastrophic cooling regime, the stagnation radius rapidly approaches the surface of the starburst region, as one considers more massive starbursts. This leads to larger accretion rates onto theSMBHand concurrently to powerfulwinds able to inhibit interstellarmatter from approaching theNSB.Our self-consistent model thus establishes a direct physical link between the SMBH accretion rate and the nuclear star formation activity of the host galaxy and provides a good upper limit to the accretion rate onto the central black hole.