we concentrate on the comparison with the Milky Way extinction curve below. For more comprehensive comparison, we need a more sophisticated model of the evolution of grain compositions [@2016PASJ...68...94H], which is left for a future work. To concentrate on the extinction curve shape, the extinction is normalized to the value in the $V$ band ($\lambda ^{-1}=1.8\,\mu {\rm m}^{-1}$); that is, we output $A_\lambda /A_V$ (so that $L$ is cancelled out).

Results {#sec:result}
=======

Evolution of grain size distribution {#evolution-of-grain-size-distribution}
------------------------------------

### Dense and diffuse ISM {#subsubsec:dense_diffuse}

We show the general features in the evolution of grain size distribution. This also serves as a test against the post-processing results in HA19. We choose the gas particles contained in $0<R<7\,{\rm kpc}$ and $|z|<0.3\,{\rm kpc}$, where we adopt a cylindrical coordinate with $R$ and $z$ being the radial and vertical coordinates, respectively ($z=0$ is the disc plane). In order to investigate the dependence on the local physical condition, we divide the gas particles into two categories: the dense (cold) and diffuse (warm) gas. The dense (cold) gas particles are chosen by $T_\mathrm{gas}< 10^{3}$K and $n_\mathrm{H}> 10\,{\rm cm}^{-3}$, while the diffuse (warm) ones by $0.1<n_\mathrm{H}<1$cm$^{-3}$ and $10^3 <T_\mathrm{gas} <10^4$K. These criteria are the same 