We compute the evolution of interstellar dust in a hydrodynamical simulation of an isolated disc galaxy. We newly implement the evolution of grain size distribution formulated and developed in our previous studies, and solve it consistently with the chemical enrichment of the galaxy. This enables us to theoretically investigate spatially resolved evolution of grain size distribution in a galaxy. The grain size distribution evolves from a large-grain-dominated (> 0.1 μm) phase to a small-grain production phase, eventually converging to a power-law-like grain size distribution similar to the so-called MRN distribution. We find a significant difference between the dense and diffuse interstellar medium (ISM): the small-grain abundance is larger in the dense ISM in the early epoch (t < 1 Gyr) because of efficient dust growth by accretion, while coagulation makes the small grain abundance less enhanced in the dense ISM later. This predicts that extinction curves are steeper in the dense ISM than in the diffuse
medium in the early phase while it becomes opposite later. The radial trend is also described by faster evolution in the inner part. We also confirmed that we reproduce the observed trend in the relation between dust-to-gas ratio and metallicity, and in the radial gradient of dust-to-gas ratio and dust-to-metal ratio. Finally, we examine the extinction curves predicted by our models, finding that the dense ISM has steeper extinction curves in the early epoch then in the dense ISM while the trend becomes opposite later.