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 f
ormation 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.
