  Dust growth is often neglected when building models of protoplanetary disks
due to its complexity and computational expense. However, it does play a major
role in shaping the evolution of protoplanetary dust and planet formation. In
this paper, we present a numerical model coupling 2-D hydrodynamic evolution of
a protoplanetary disk, including a Jupiter-mass planet, and dust coagulation.
This is obtained by including multiple dust fluids in a single grid-based
hydrodynamic simulation and solving the Smoluchowski equation for dust
coagulation on top of solving for the hydrodynamic evolution. We find that
fragmentation of dust aggregates trapped in a pressure bump outside of the
planetary gap leads to an enhancement in density of small grains. We compare
the results obtained from the full coagulation treatment to the commonly used,
fixed dust size approach and to previously applied, less computationally
intensive methods for including dust coagulation. We find that the full
coagulation results cannot be reproduced using the fixed-size treatment, but
some can be mimicked using a relatively simple method for estimating the
characteristic dust size in every grid cell.
