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In the recent years, sub/mm observations of protoplanetary disks havediscovered an incredible diversity of substructures in the dust emission. Animportant result was the finding that dust grains of mm size are embedded invery thin dusty disks. This implies that the dust mass fraction in the midplanebecomes comparable to the gas, increasing the importance of the interactionbetween the two components there. We address this problem by means of numerical2.5D simulations in order to study the gas and dust interaction in fully globalstratified disks. To this purpose, we employ the recently developed dust grainmodule 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 constantStokes number of $St=0.01$ and $St=0.1$, corresponding to grains with sizes of0.9 cm and 0.9 mm, respectively, for the given disk model. By injecting aconstant pebble flux at the outer domain, the system reaches a quasi steadystate of turbulence and dust concentrations driven by the streaminginstability. For our given setup and using resolutions up to 2500 cells perscale height we resolve the streaming instability, leading to local dustclumping and concentrations. Our results show dust density values of around10-100 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 themodels with $\mathit{St}=0.01$ and $\mathit{St}=0.1$. The grain size and pebbleflux for model $\mathit{St}=0.01$ compares well with dust evolution models ofthe first million years of disk evolution. For those grains the scatter opacitydominates the extinction coefficient at mm wavelengths. These types of globaldust and gas simulations are a promising tool for studies of the gas and dustevolution at pressure bumps in protoplanetary disks.

Streaming instability in a global patch simulation of protoplanetary disks