  We explore analytically and numerically agglomeration driven by advection and
localized source. The system is inhomogeneous in one dimension, viz. along the
direction of advection. We analyze a simplified model with mass-independent
advection velocity, diffusion coefficient, and reaction rates. We also examine
a model with mass-dependent coefficients describing aggregation with
sedimentation. For the simplified model, we obtain an exact solution for the
stationary spatially dependent agglomerate densities. In the model describing
aggregation with sedimentation, we report a new conservation law and develop a
scaling theory for the densities. For numerical efficiency we exploit the
low-rank approximation technique; this dramatically increases the computational
speed and allows simulations of large systems. The numerical results are in
excellent agreement with the predictions of our theory.
