  It was previously shown that the superdroplet algorithm for modeling the
collision-coalescence process can faithfully represent mean droplet growth in
turbulent clouds. But an open question is how accurately the superdroplet
algorithm accounts for fluctuations in the collisional aggregation process.
Such fluctuations are particularly important in dilute suspensions. Even in the
absence of turbulence, Poisson fluctuations of collision times in dilute
suspensions may result in substantial variations in the growth process,
resulting in a broad distribution of growth times to reach a certain droplet
size. We quantify the accuracy of the superdroplet algorithm in describing the
fluctuating growth history of a larger droplet that settles under the effect of
gravity in a quiescent fluid and collides with a dilute suspension of smaller
droplets that were initially randomly distributed in space ('lucky droplet
model'). We assess the effect of fluctuations upon the growth history of the
lucky droplet and compute the distribution of cumulative collision times. The
latter is shown to be sensitive enough to detect the subtle increase of
fluctuations associated with collisions between multiple lucky droplets. The
superdroplet algorithm incorporates fluctuations in two distinct ways: through
the random spatial distribution of superdroplets and through the Monte Carlo
collision algorithm involved. Using specifically designed numerical
experiments, we show that both on their own give an accurate representation of
fluctuations. We conclude that the superdroplet algorithm can faithfully
represent fluctuations in the coagulation of droplets driven by gravity.
