  Due to the non-axisymmetric potential of the central bar, barred spiral
galaxies form, in addition to their characteristic arms and bar, a variety of
structures within the thin gas disk, like nuclear rings, inner spirals and
dust-lanes. These structures in the inner kiloparsec are most important to
explain and understand the rate of black hole feeding. The aim of this work is
to investigate the influence of stellar bars in spiral galaxies on the thin
self-gravitating gas disk. We focus on the accretion of gas onto the central
supermassive black hole and its time-dependent evolution. We conduct
multi-scale simulations simultaneously resolving the galactic disk and the
accretion disk around the central black-hole. We vary in all simulations the
initial gas disk mass. As additional parameter we choose either the gas
temperature for isothermal simulations or the cooling timescale in case of
non-isothermal simulations. Accretion is either driven by a gravitationally
unstable or clumpy accretion disk or by energy dissipation in strong shocks.
Most simulations show a strong dependence of the accretion rate at the outer
boundary of the central accretion disk ($r< 300~\mathrm{pc}$) on the gas flow
at kiloparsec scales. The final black hole masses reach up to $\sim 10^9
M_\odot$ after $1.6~\mathrm{Gyr}$. Our models show the expected influence of
the Eddington limit and a decline in growth rate at the corresponding
sub-Eddington limit.
