To investigate the evolution of dust in a cosmological volume, we perform hydrodynamic simulations, in which the enrichment of metals and dust is treated self-consistently with star formation and stellar feedback. We consider dust evolution driven by dust production in stellar ejecta, dust destruction by sputtering, grain growth by accretion and coagulation, and grain disruption by shattering, and treat small and large grains separately to trace the grain size distribution. After confirming that our model nicely reproduces the observed relation between dust-to-gas ratio and metallicity for nearby galaxies, we concentrate on the dust abundance over the cosmological volume in this paper. The comoving dust mass density has a peak at redshift $z\sim 1$--2, coincident with the observationally suggested dustiest epoch in the Universe. {In the local Universe}, roughly 10 per cent of the dust is contained in the intergalactic medium (IGM), where only 1/3--1/4 of the dust survives against dust destruction by sputtering. We also show that the dust mass function is roughly reproduced at $\lesssim 10^8$ M$_\odot$, while the massive end still has a discrepancy, which indicates {the necessity of stronger feedback in massive galaxies}. %%The relation showed that accretion is essential for dusty galaxies. In addition, our model broadly reproduces the observed radial profile of dust surface density in the circum-galactic medium (CGM). While our model satisfies the observational constraints for the dust extinction {on cosmological scales}, it predicts that the dust in the CGM and IGM is dominated by large ($> 0.03~μ$m) grains, which is in tension with the steep reddening curves {observed} in the CGM.

17 pages, 9 figures. published on MNRAS