  We use lattice Boltzmann simulations, in conjunction with Ewald summation
methods, to investigate the role of hydrodynamic interactions in colloidal
suspensions of dipolar particles, such as ferrofluids. Our work addresses
volume fractions $\phi$ of up to 0.20 and dimensionless dipolar interaction
parameters $\lambda$ of up to 8. We compare quantitatively with Brownian
dynamics simulations, in which many-body hydrodynamic interactions are absent.
Monte Carlo data are also used to check the accuracy of static properties
measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic
interactions slow down both the long-time and the short-time decays of the
intermediate scattering function $S(q,t)$, for wavevectors close to the peak of
the static structure factor $S(q)$, by a factor of roughly two. The long-time
slowing is diminished at high interaction strengths whereas the short-time
slowing (quantified via the hydrodynamic factor $H(q)$) is less affected by the
dipolar interactions, despite their strong effect on the pair distribution
function arising from cluster formation. Cluster formation is also studied in
transient data following a quench from $\lambda = 0$; hydrodynamic interactions
slow the formation rate, again by a factor of roughly two.
