  Turbulence is argued to play a crucial role in cloud droplet growth. The
combined problem of turbulence and cloud droplet growth is numerically
challenging. Here, an Eulerian scheme based on the Smoluchowski equation is
compared with two Lagrangian superparticle (or su- perdroplet) schemes in the
presence of condensation and collection. The growth processes are studied
either separately or in combination using either two-dimensional turbulence, a
steady flow, or just gravitational acceleration without gas flow. Good
agreement between the differ- ent schemes for the time evolution of the size
spectra is observed in the presence of gravity or turbulence. Higher moments of
the size spectra are found to be a useful tool to characterize the growth of
the largest drops through collection. Remarkably, the tails of the size spectra
are reasonably well described by a gamma distribution in cases with gravity or
turbulence. The Lagrangian schemes are generally found to be superior over the
Eulerian one in terms of computational performance. However, it is shown that
the use of interpolation schemes such as the cloud-in-cell algorithm is
detrimental in connection with superparticle or superdroplet approaches.
Furthermore, the use of symmetric over asymmetric collection schemes is shown
to reduce the amount of scatter in the results.
