  Black holes grow by accreting matter from their surroundings. However,
angular momentum provides an efficient natural barrier to accretion and so only
the lowest angular momentum material will be available to feed the black holes.
The standard sub-grid model for black hole accretion in galaxy formation
simulations - based on the Bondi-Hoyle method - does not account for the
angular momentum of accreting material, and so it is unclear how representative
the black hole accretion rate estimated in this way is likely to be. In this
paper we introduce a new sub-grid model for black hole accretion that naturally
accounts for the angular momentum of accreting material. Both the black hole
and its accretion disc are modelled as a composite accretion disc particle. Gas
particles are captured by the accretion disc particle if and only if their
orbits bring them within its accretion radius R_acc, at which point their mass
is added to the accretion disc and feeds the black hole on a viscous timescale
t_visc. The resulting black hole accretion rate (dM/dt)_BH powers the accretion
luminosity L_acc ~ (dM/dt)_BH, which drives black hole feedback. Using a series
of controlled numerical experiments, we demonstrate that our new accretion disc
particle method is more physically self-consistent than the Bondi-Hoyle method.
We also discuss the physical implications of the accretion disc particle method
for systems with a high degree of rotational support, and we argue that the
M_BH-sigma relation in these systems should be offset from the relation for
classical bulges and ellipticals, as appears to be observed.
