Three dimensional numerical simulation of the transient turbulent jet and ignition processes of a premixed methane-air mixture of a turbulent jet ignition (TJI) system is performed using Converge computational software. The prechamber initiated combustion enhancement technique that is utilized in a TJI system enables low temperature combustion by increasing the flame propagation rate and therefore decreasing the burn duration. Two important components of the TJI system are the prechamber where the spark plug and injectors are located and the nozzle which connects the prechamber to the main chamber. In order to model the turbulent jet of the TJI system, RANS k-ε and LES turbulent models and the SAGE chemistry solver with a reduced mechanism for methane are used.This research aims to give further insight into the turbulent jet flow in the TJI system by showing the numerical results of the jet temperature, turbulent kinetic energy and pressure which is compared to corresponding experimental measurements. A comparison is also made between the numerical contours and the optical images obtained from combustion visualization experiments in an optically accessible Rapid Compression Machine (RCM). To choose the most suitable mechanism for the simulation, four detailed mechanisms along with a reduced one are employed and the numerical pressure traces are compared with the experiments. Results show that the ignition delay time and burn rate provided by the mechanisms are in comparably acceptable agreement with the experimental results.