  We use cosmological smoothed-particle hydrodynamics (SPH) simulations of the
Lambda cold dark matter (CDM) model to study the abundance of damped
Lyman-alpha absorbers (DLAs) in the redshift range z=0-4.5. We compute the
cumulative DLA abundance by using the relation between DLA cross-section and
the total halo mass inferred from the simulations. Our approach includes a
phenomenological model of galactic wind. We employ the ``conservative entropy''
formulation of SPH, and utilise a series of simulations of varying box-size and
particle number to isolate the impact of numerical resolution on our results.
We show that the DLA abundance was overestimated in previous studies for three
reasons: (1) the overcooling of gas occurring with non-conservative
formulations of SPH, (2) a lack of numerical resolution, and (3) an inadequate
treatment of feedback. Our new results for the total neutral hydrogen mass
density, DLA abundance, and column density distribution function all agree
reasonably well with observational estimates at redshift z=3, indicating that
DLAs arise naturally from radiatively cooled gas in dark matter haloes that
form in a Lambda CDM universe. Our simulations suggest a moderate decrease in
DLA abundance by roughly a factor of two from z=4.5 to 3, consistent with
observations. A significant decline in abundance from z=3 to z=1, followed by
weak evolution from z=1 to z=0, is also indicated, but our low-redshift results
need to be interpreted with caution because they are based on coarser
simulations than the ones employed at high redshift. Our highest resolution
simulation also suggests that the halo mass-scale below which DLAs do not exist
is slightly above 10^8 Msun/h at z=3-4, somewhat lower than previously
estimated. (abridged)
