$a\lesssim 0.03~\micron$]{} because small grains have larger surface-to-volume ratios (recall that the accretion rate is proportional to the grain surface area). Accretion is saturated when a significant fraction of gas-phase metals are used up; and subsequently, coagulation converts small grains into large grains, smoothing the grain size distribution towards a power-law shape similar to the @1977ApJ...217..425M [hereafter MRN] grain size distribution.

In reality, the evolution of dust is strongly affected by the ambient physical condition such as gas metallicity, temperature, and density. Although [@2013MNRAS.432..637A] succeeded in calculating the evolution of grain size distribution, their one-zone model is not capable of treating the spatial variation of dust evolution that depends on the ISM conditions. The evolution of ISM is governed by hydrodynamical processes. Thus, hydrodynamic simulations have been used to study the evolution of ISM in galaxies [e.g. @2007ApJ...660..276W; @2008PASJ...60..667S; @2014MNRAS.442.3745M; @2014ApJS..210...14K; @2016ApJ...833..202K; @2019arXiv190508806M; @2019MNRAS.490.1425L; @2019arXiv190907388G]. For the purpose of considering the effects of ISM evolution on dust properties, it would be ideal to treat dust evolution in a manner consistent with the hydrodynamical development of the ISM. However, it is in general computationally expensive to implement the evolution of grain size distribution in already heavy hydrodynamic simulations.

In the past, 