Indiana University-Purdue University Indianapolis (IUPUI) / Ignition of a combustible mixture by a transient jet of hot reactive gas is important for safety of mines, pre-chamber ignition in IC engines, detonation initiation, and in novel constant-volume combustors. The present work is a numerical study of the hot-jet ignition process in a long constant-volume combustor (CVC) that represents a wave-rotor channel. The mixing of hot jet with cold mixture in the main chamber is first studied using non-reacting simulations. The stationary and traversing hot jets of combustion products from a pre-chamber is injected through a converging nozzle into the main CVC chamber containing a premixed fuel-air mixture. Combustion in a two-dimensional analogue of the CVC chamber is modeled using global reaction mechanisms, skeletal mechanisms, and detailed reaction mechanisms for four hydrocarbon fuels: methane, propane, ethylene, and hydrogen. The jet and ignition behavior are compared with high-speed video images from a prior experiment. Hybrid turbulent-kinetic schemes using some skeletal reaction mechanisms and detailed mechanisms are good predictors of the experimental data. Shock-flame interaction is seen to significantly increase the overall reaction rate due to baroclinic vorticity generation, flame area increase, stirring of non-uniform density regions, the resulting mixing, and shock compression. The less easily ignitable methane mixture is found to show higher ignition delay time compared to slower initial reaction and greater dependence on shock interaction than propane and ethylene. The confined jet is observed to behave initially as a wall jet and later as a wall-impinging jet. The jet evolution, vortex structure and mixing behavior are significantly different for traversing jets, stationary centered jets, and near-wall jets. Production of unstable intermediate species like C2H4 and CH3 appears to depend significantly on the initial jet location while relatively stable species like OH are less sensitive. Inclusion of minor radical species in the hot-jet is observed to reduce the ignition delay by 0.2 ms for methane mixture in the main chamber. Reaction pathways analysis shows that ignition delay and combustion progress process are entirely different for hybrid turbulent-kinetic scheme and kinetics-only scheme.