Gong, HaoIn this thesis we present a unified model for dense core formation and collapse within post-shock dense layers inside giant molecular clouds. Supersonic converging flows collide to compress low density gas to high density clumps, inside which gravitational collapse can happen. We consider both spherically symmetric and planar converging flows, and run models with inflow Mach number from 1.1-9 to investigate the relation between core properties and the bulk velocity dispersion of the mother cloud. Four stages of protostar formation are identified: core building, core collapse, envelope infall, and late accretion. The core building stage takes 10 times as long as core collapse, which lasts a few 10<super>5</super> yr, consistent with observed prestellar core lifetimes. We find that the density profiles of cores during collapse can be fitted by Bonnor-Ebert sphere profiles, and that the density and velocity profiles approach the Larson-Penston solution at the core collapse instant. Core shapes change from oblate to prolate as they evolve. Cores with masses varying by three orders of magnitude ~ 0.05 - 50 solar mass are identified in our high Mach number simulations, and a much smaller mass range for models having low Mach number. The median core mass versus Mach number lies between the minimum mass that can collapse in late times Ma<super>-1</super> and the most evolved core mass Ma<super>-1/2</super>. We implement sink particles to the grid code Athena to track the collapse of other dense regions of a large scale simulation after the most evolved core collapses, We demonstrate use of our code for applications with a simulation of planar converging supersonic turbulent flows, in which multiple cores form and collapse to create sinks; these sinks continue to interact and accrete from their surroundings over several Myr.DissertationAstrophysicscore formationgravitystar formationturbulence