High pressure hydrogen leak is one of the top safety issues presently. This study elucidates the physics and mechanism of high pressure hydrogen jet ignition when the hydrogen suddenly spouts into the air. The experimental work was done elsewhere, while we did the numerical work on this high pressure hydrogen leak problem. The direct numerical simulation based on the compressible fluid dynamics considering viscous effect was carried out with the two-dimensional axisymmetric coordinate system. A detailed model of hydrogen reaction is applied and a narrow tube attached to a high pressure reservoir is assumed in the numerical simulation. The exit of the tube is opened in the atmosphere. When high pressure hydrogen is passing through the tube filled by atmospheric air, a strong shock wave is formed and heats up hydrogen behind the shock wave by compression effect. The leading shock wave is expanded widely after the exit, hydrogen then mixed with air by several vortices generated around the exit of the tube. As a result, a couple of auto-ignitions of hydrogen occur. It is found that there is a certain relationship between the auto-ignition and tube length. When the tube becomes longer, the tendency of auto-ignition is increased. Additionally, other type of auto-ignitions is predicted. An explosion is also occurred in the tube under a certain condition. Vortex is generated behind the shock wave in the long tube. There is a possibility of an auto-ignition induced by vortices.