  Reconstructing the galaxy peculiar velocity field from the distribution of
large-scale structure plays an important role in cosmology. On one hand, it
gives us an insight into structure formation and gravity; on the other, it
allows us to selectively extract the kinetic Sunyaev-Zeldovich (kSZ) effect
from cosmic microwave background (CMB) maps. In this work, we employ
high-accuracy synthetic galaxy catalogs on the light cone to investigate how
well we can recover the velocity field when utilizing the three-dimensional
spatial distribution of the galaxies in a modern large-scale structure
experiment such as the Dark Energy Spectroscopic Instrument (DESI) and Rubin
Observatory (LSST). In particular, we adopt the standard technique used in
baryon acoustic oscillation (BAO) analysis for reconstructing the Zeldovich
displacements of galaxies through the continuity equation, which yields a
first-order approximation to their large-scale velocities. We investigate
variations in the number density, bias, mask, area, redshift noise, and survey
depth, and smoothing. Since our main goal is to provide guidance for planned
kSZ analysis between DESI and the Atacama Cosmology Telescope (ACT), we apply
velocity reconstruction to a faithful representation of DESI spectroscopic and
photometric targets. We report the cross-correlation coefficient between the
reconstructed and the true velocities along the line of sight. For the DESI Y1
spectroscopic survey, we expect the correlation coefficient to be $r \approx
0.64$, while for a photometric survey with $\sigma_z/(1+z) = 0.02$, as is
approximately the case for the Legacy Survey used in the target selection of
DESI galaxies, $r$ shrinks by half to $r \approx 0.31$. We hope the results in
this paper can be used to inform future kSZ stacking studies. All scripts used
in this paper can be found here:
\url{https://github.com/boryanah/abacus_kSZ_recon}.
