Hydrogen (H2) has become a key in the decarbonation process of the aeronautical field and new gaseous injection systems must be designed to suit hydrogen’s specific properties (high laminar flame speed, high adiabatic temperature, large flammability limits and fast diffusivity (Le<1)). In this study, Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) are performed for a co-axial injector including an annular premixed hydrogen–air, swirled injection surrounding a central axial pure hydrogen lance. LES of the injector installed in a full chamber are performed at 12bar and the LES resolution issues associated with these high pressures are presented. LES reveals that the flame is stabilized on the rim separating the premixed and the pure hydrogen streams. The stabilization is produced by a structure called RSE for Rim Stabilized Edge Flame. To avoid resolution issues of the LES, the RSE flame structure is analyzed using CANTERA 1D flames and a 2D DNS of the attachment region. Extinction limits are described and implications for flame stability are discussed.