  Dust is a major component of protoplanetary and debris disks as it is the
main observable signature of planetary formation. However, since dust dynamics
is size-dependent (because of gas-drag or radiation pressure) any attempt to
understand the full dynamical evolution of circumstellar dusty-disks that
neglect the coupling of collisional evolution with dynamical evolution is
thwarted because of the feedback between these two processes. Here, a new
hybrid lagrangian/eulerian code is presented that overcomes some of these
difficulties. The particles representing "dust-clouds" are tracked individually
in a lagrangian way. This system is then mapped on an eulerian spatial grid,
inside the cells of which the local collisional evolutions are computed.
Finally, the system is remapped back in a collection of discrete lagrangian
particles keeping constant their number. An application example on dust growth
in a turbulent protoplanetary disk at 1 AU is presented. First the growth of
dust is considered in the absence of a dead-zone and the vertical distribution
of dust is self-consistently computed. It is found that the mass is rapidly
dominated by particles about a fraction of millimeter in size. Then the same
case with an embedded dead-zone is investigated and It is found that
coagulation is much more efficient and produces, in a short time scale,
1cm-10cm dust pebbles that dominate the mass. These pebbles may then be
accumulated into embryos sized objects inside large-scale turbulent structures
as shown recently (see e.g. Johansen et al., 2007).
