  When a supermassive black hole exists in the centre of a galaxy, an
additional inner Lindblad resonance (ILR) exists inside the usual ILRs. We
study gas dynamics in a weakly barred potential with a central supermassive
black hole by using 2D numerical simulations, and we investigate the effect of
the additional ILR on fuelling gas into nuclear starburst regions or AGNs. Our
numerical results show that strong trailing spiral shocks are formed at the
resonance region, and the gas in the shock region is rapidly fuelled into a
central region and make a nuclear gas ring. As a result, a large amount of gas
is concentrated in the nuclear region beyond the ILR in a dynamical time scale.
