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We present the first 2D hydrodynamical finite volume simulations in whichdust is fully coupled with the gas, including its back-reaction onto it, and atthe same time the dust size is evolving according to coagulation andfragmentation based on a sub-grid model. The aim of this analysis is to presentthe differences occurring when dust evolution is included relative tosimulations with fixed dust size, with and without an embedded Jupiter-massplanet that triggers gap formation. We use the two-fluid polar Godunov-typecode RoSSBi developed by Surville et al. 2016 combined with a new localsub-grid method for dust evolution based on the model by Birnstiel et al. 2012.We find striking differences between simulations with variable and fixed dustsizes. The timescales for dust depletion differ significantly and yield acompletely different evolution of the dust surface density. In general sharpfeatures such as pile-ups of dust in the inner disk and near gap edges, when amassive planet is present, become much weaker. This has important implicationson the interpretation of observed substructure in disks, suggesting that thepresence of a massive planet does not necessarily cause sharp gaps and rings inthe dust component. Also, particles with different dust sizes show a differentdistribution, pointing to the importance of multi-wavelength syntheticobservations in order to compare with observations by ALMA and otherinstruments. We also find that simulations adopting fixed intermediate particlesizes, in the range $10^{-2} - 10^{-1}$ cm, best approximate the surfacedensity evolution seen in simulations with dust evolution.

A sub-grid model for the growth of dust particles in hydrodynamical simulations of protoplanetary disks