  We investigate prestellar core formation and accretion based on
three-dimensional hydrodynamic simulations. Our simulations represent local
$\sim 1$pc regions within giant molecular clouds where a supersonic turbulent
flow converges, triggering star formation in the post-shock layer. We include
turbulence and self-gravity, applying sink particle techniques, and explore a
range of inflow Mach number ${\cal M}=2-16$. Two sets of cores are identified
and compared: $t_1$-cores are identified of a time snapshot in each simulation,
representing dense structures in a single cloud map; $t_\mathrm{coll}$-cores
are identified at their individual time of collapse, representing the initial
mass reservoir for accretion. We find that cores and filaments form and evolve
at the same time. At the stage of core collapse, there is a well-defined,
converged characteristic mass for isothermal fragmentation that is comparable
to the critical Bonner-Ebert mass at the post-shock pressure. The core mass
functions (CMFs) of $t_\mathrm{coll}$-cores show a deficit of high-mass cores
($\gtrsim 7M_\odot$) compared to the observed stellar initial mass function
(IMF). However, the CMFs of $t_1$-cores are similar to the observed CMFs and
include many low-mass cores that are gravitationally stable. The difference
between $t_1$-cores and $t_\mathrm{coll}$-cores suggests that the full sample
from observed CMFs may not evolve into protostars. Individual sink particles
accrete at a roughly constant rate throughout the simulations, gaining one
$t_\mathrm{coll}$-core mass per free-fall time even after the initial mass
reservoir is accreted. High-mass sinks gain proportionally more mass at late
times than low-mass sinks. There are outbursts in accretion rates, resulting
from clumpy density structures falling into the sinks.
