  We perform smoothed particle hydrodynamics (SPH) simulations of an isolated
galaxy with a new treatment for dust formation and destruction. To this aim, we
treat dust and metal production self-consistently with star formation and
supernova feedback. For dust, we consider a simplified model of grain size
distribution by representing the entire range of grain sizes with large and
small grains. We include dust production in stellar ejecta, dust destruction by
supernova (SN) shocks, grain growth by accretion and coagulation, and grain
disruption by shattering. We find that the assumption of fixed dust-to-metal
mass ratio becomes no longer valid when the galaxy is older than 0.2 Gyr, at
which point the grain growth by accretion starts to contribute to the nonlinear
rise of dust-to-gas ratio. As expected in our previous one-zone model,
shattering triggers grain growth by accretion since it increases the total
surface area of grains. Coagulation becomes significant when the galaxy age is
greater than $\sim$ 1 Gyr: at this epoch the abundance of small grains becomes
high enough to raise the coagulation rate of small grains. We further compare
the radial profiles of dust-to-gas ratio $(\mathcal{D})$ and dust-to-metal
ratio $(\mathcal{D}/Z)$ (i.e., depletion) at various ages with observational
data. We find that our simulations broadly reproduce the radial gradients of
dust-to-gas ratio and depletion. In the early epoch ($\lesssim 0.3$ Gyr), the
radial gradient of $\mathcal{D}$ follows the metallicity gradient with
$\mathcal{D}/Z$ determined by the dust condensation efficiency in stellar
ejecta, while the $\mathcal{D}$ gradient is steeper than the $Z$ gradient at
the later epochs because of grain growth by accretion. The framework developed
in this paper is applicable to any SPH-based galaxy evolution simulations
including cosmological ones.
