  In the recent years, sub/mm observations of protoplanetary disks have
discovered an incredible diversity of substructures in the dust emission. An
important result was the finding that dust grains of mm size are embedded in
very thin dusty disks. This implies that the dust mass fraction in the midplane
becomes comparable to the gas, increasing the importance of the interaction
between the two components there. We address this problem by means of numerical
2.5D simulations in order to study the gas and dust interaction in fully global
stratified disks. To this purpose, we employ the recently developed dust grain
module in the PLUTO code. Our model focuses on a typical T Tauri disk model,
simulating a short patch of the disk at 10 au which includes grains of constant
Stokes number of $St=0.01$ and $St=0.1$, corresponding to grains with sizes of
0.9 cm and 0.9 mm, respectively, for the given disk model. By injecting a
constant pebble flux at the outer domain, the system reaches a quasi steady
state of turbulence and dust concentrations driven by the streaming
instability. For our given setup and using resolutions up to 2500 cells per
scale height we resolve the streaming instability, leading to local dust
clumping and concentrations. Our results show dust density values of around
10-100 times the gas density with a steady state pebble flux between $3.5
\times 10^{-4}$ and $2.5 \times 10^{-3} M_{\rm Earth}/\mathit{year}$ for the
models with $\mathit{St}=0.01$ and $\mathit{St}=0.1$. The grain size and pebble
flux for model $\mathit{St}=0.01$ compares well with dust evolution models of
the first million years of disk evolution. For those grains the scatter opacity
dominates the extinction coefficient at mm wavelengths. These types of global
dust and gas simulations are a promising tool for studies of the gas and dust
evolution at pressure bumps in protoplanetary disks.
