We study the destruction of interstellar dust via sputtering in supernova ( SN ) shocks using three-dimensional hydrodynamical simulations .
With a novel numerical framework , we follow both sputtering and dust dynamics governed by direct collisions , plasma drag and betatron acceleration .
Grain-grain collisions are not included and the grain-size distribution is assumed to be fixed .
The amount of dust destroyed per SN is quantified for a broad range of ambient densities and fitting formulae are provided .
Integrated over the grain-size distribution , nonthermal ( inertial ) sputtering dominates over thermal sputtering for typical ambient densities .
We present the first simulations that explicitly follow dust sputtering within a turbulent multiphase interstellar medium .
We find that the dust destruction timescales \tau are 0.35 Gyr for silicate dust and 0.44 Gyr for carbon dust in solar neighborhood conditions .
The SN environment has an important impact on \tau .
SNe that occur in preexisting bubbles destroy less dust as the destruction is limited by the amount of dust in the shocked gas .
This makes \tau about 2.5 times longer than the estimate based on results from a single SN explosion .
We investigate the evolution of the dust-to-gas mass ratio ( DGR ) , and find that a spatial inhomogeneity of \sim 14 % develops for scales below 10 pc .
It locally correlates positively with gas density but negatively with gas temperature even in the exterior of the bubbles due to incomplete gas mixing .
This leads to a \sim 30 % lower DGR in the volume filling warm gas compared to that in the dense clouds .