  We study evolution of voids in cosmological simulations using a new method
for tracing voids over cosmic time. The method is based on tracking watershed
basins (contiguous regions around density minima) of well developed voids at
low redshift, on a regular grid of density field. It enables us to construct a
robust and continuous mapping between voids at different redshifts, from
initial conditions to the present time. We discuss how the new approach
eliminates strong spurious effects of numerical origin when voids evolution is
traced by matching voids between successive snapshots (by analogy to halo
merger trees). We apply the new method to a cosmological simulation of a
standard LambdaCDM cosmological model and study evolution of basic properties
of typical voids (with effective radii between 6Mpc/h and 20Mpc/h at redshift
z=0) such as volumes, shapes, matter density distributions and relative
alignments. The final voids at low redshifts appear to retain a significant
part of the configuration acquired in initial conditions. Shapes of voids
evolve in a collective way which barely modifies the overall distribution of
the axial ratios. The evolution appears to have a weak impact on mutual
alignments of voids implying that the present state is in large part set up by
the primordial density field. We present evolution of dark matter density
profiles computed on iso-density surfaces which comply with the actual shapes
of voids. Unlike spherical density profiles, this approach enables us to
demonstrate development of theoretically predicted bucket-like shape of the
final density profiles indicating a wide flat core and a sharp transition to
high-density void walls.
