The primary breakup of a planar liquid sheet produced by an air-blast atomizer was studied through numerical simulations, in order to reveal physical mechanisms involved during this process. The reliability of simulations was verified by comparing the macroscopic parameters, e.g. breakup time and spatial growth rate, with experimental data. Shear instability and RT (Rayleigh-Taylor) instability were found to play important roles during the primary breakup. By analyzing the acceleration of a fluid parcel within liquid sheet using Discrete Particle Method, and measuring the wave length of transverse unstable wave, RT instability was found to be partially responsible for transverse instability. The predictions of LISA (Linearized Instability Sheet Atomization) model on breakup time were compared to experiments, and obvious differences were found to exist. By analyzing the velocity distribution around liquid sheet and the variation of the amplitude of unstable wave versus spatial position, the reasons why LISA's predictions differ from experiments were partially revealed, and the perspectives to improve LISA model to get better accuracy were suggested.