This work focuses on the experimental and numerical investigation of maximum overpressure and pressure dynamics during ignited hydrogen releases in a storage enclosure, e.g., in marine vessel or rail carriage, with limited vent size area, i.e., the pressure peaking phenomenon (PPP) revealed theoretically at Ulster University in 2010. The CFD model previously validated against small scale experiments in a 1 m³ enclosure is employed here to simulate real-scale tests performed by the University of South-Eastern Norway (USN) in a chamber with a volume of 15 m³. The numerical study compares two approaches on how to model the ignited hydrogen release conditions for under-expanded jets: (1) notional nozzle concept model with inflow boundary condition, and (2) volumetric source model in the governing conservation equations. For the test with storage pressure of 11.78 MPa, both approaches reproduce the experimental pressure dynamics and the pressure peak with a maximum 3% deviation. However, the volumetric source approach reduces significantly the computational time by approximately 3 times (CFL = 0.75). The sensitivity analysis is performed to study the effect of CFL number, the size of the volumetric source and number of iterations per time step. An approach based on the use of a larger size volumetric source and uniform coarser grid with a mesh size of a vent of square size is demonstrated to reduce the duration of simulations by a factor of 7.5 compared to the approach with inflow boundary at the notional nozzle exit. The volumetric source model demonstrates good engineering accuracy in predicting experimental pressure peaks with deviation from −14% to +11% for various release and ventilation scenarios as well as different volumetric source sizes. After validation against experiments, the CFD model is employed to investigate the effect of cryogenic temperature in the storage on the overpressure dynamics in the enclosure. For a storage pressure equal to 11.78 MPa, it is found that a decrease of storage temperature from 277 K to 100 K causes a twice larger pressure peak in the enclosure due to the pressure peaking phenomenon.