Flame stabilization in the DLR hydrogen supersonic combustor with strut injection was numerically investigated by using an in-house large eddy simulation code developed on the OpenFoam platform. To facilitate the comparison and analysis of various hydrogen oxidation mechanisms with different levels of mechanism reduction, the proposed 2D calculation model was validated against both the 3D simulation and the experimental data. The results show that the 2D model can capture the DLR flow and combustion characteristics with satisfactorily quantitative accuracy and significantly less computational load. By virtue of the flow visualization and the analyses of species evolution and heat release, the supersonic combustion in the DLR combustor can be divided into three stages along the streamwise direction: the induction stage where ignition occurs and active radicals are produced, the transition stage through which radicals are advected to the downstream, and the intense combustion stage where most heat release occurs. Furthermore, the sensitivity analysis of key reaction steps identifies the important role of chain carrying and heat release reactions in numerically reproducing the three-stage combustion stabilization mode in the DLR combustor.