Under-expanded jets have wide range of application from fuel injection to rocket propulsion. In the present work, a numerical model was generated to investigate the fluid mechanics behavior of under-expanded jet formation and wall interaction of a jet produced by exhausting a high pressure cylinder through a narrow tube into a low pressure cylinder. Axisymmectic, Reynolds Averaged Navier Stokes simulations were conducted employing the ANSYS FLUENT explicit, Coupled Pressure-Velocity solver to determine the stagnation pressure at the wall downstream of the orifice. Transient cases were conducted using timestep sizes of 1.0 × 10−8 s and 5.0 × 10−9 s. Various gases were investigated with Hydrogen being the primary working fluid with pressure ratios ranging from 10 to 100. This paper will focus primarily on the Hydrogen jets for pressure ratios of 10, 20, and 70. Numerical results were validated from both experimental results and higher fidelity Large Eddy Simulation results specifically analyzing the jet formation. Error between Mach disk height, Mach disk width, and Prandtl-Meyer expansion fan angles of the jet for pressure ratios of 10 and 70 were kept below 5%. The peak stagnation pressures at the center of the far wall for pressure ratios of 10, 20, and 70 were observed to be 86,843 Pa, 127,786 Pa, and 315,843 Pa, respectively. The predicted peak pressures show a linear relationship with respect to the initial pressure ratio existing between the high pressure and low pressure regions when the ratios are bounded between 10 and 70.