It is well known that NOx formation has a strong dependence on the maximum temperature and correspondingly with the maximum chamber pressure of a closed combustion system. However, in a case of impinging-jet-flame (IJF hereafter) combustion with opposed dual pre-chambers, low $NO_x$ formation with high pressure could be achieved, but its mechanism has not been clearly understood so far. In this study, a three-dimensional analysis is adopted to resolve time-variant local properties that might indicate the mechanism of IJF combustion. Numerical results are verified by comparing them with experiments. The IJF combustion in a vessel with no pre-chamber, with single pre-chamber, and with dual pre-chambers is studied. The orifice diameter and the volumetric ratio of pre-chamber are used as geometric parameters. The effects of main-chamber ignition delay time and combustion time of main-chamber, orifice exit velocity, orifice exit temperature, turbulent kinetic energy of main-chamber and spatial distribution of temperature in the latter stage of combustion are investigated. A longer main-chamber ignition delay and a shorter main-chamber combustion time suppress the formation of high temperature region with respect to mean temperature, which consequently results in less NO production.