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The way supermassive black holes (SMBH) in galactic centers accumulate theirmass is not completely determined. At large scales, it is governed by galacticencounters, mass inflows connected to spirals arms and bars, or due toexpanding shells from supernova (SN) explosions in the central parts ofgalaxies. The investigation of the latter process requires an extensive set ofgas dynamical simulations to explore the muti-dimensional parameter spaceneeded to frame the phenomenon. The aims of this paper are to extend ourinvestigation of the importance of supernovae for inducing accretion onto aSMBH and carry out a comparison between the fully hydrodynamic code Flash andthe much less computationally intensive code Ring, which uses the thin shellapproximation. We simulate 3D expanding shells in a gravitational potentialsimilar to that of the Galactic Center with a variety of homogeneous andturbulent environments. In homogeneous media, we find convincing agreementbetween Flash and Ring in the shapes of shells and their equivalent radiithroughout their whole evolution until they become subsonic. In highlyinhomogeneous, turbulent media, there is also a good agreement of shapes andsizes of shells, and of the times of their first contact with the central 1 pcsphere, where we assume that they join the accretion flow. The comparisonsupports the proposition that a SN occurring at a galactocentric distance of 5pc typically drives 1 - 3 $M_\odot$ into the central 1 pc around the galacticcenter.

Flash-light on the Ring: hydrodynamic simulations of expandingsupernova shells near supermassive black holes