Detailed understanding of the physical processes occurring in the combustor of a scramjet engine is crucial for enabling this technology and is considered the most promising for hypersonic flight. Laboratory, ground testing, and flight-testing experiments, together with simulations, comprise the tools available to fill the current gap in scramjet combustor knowledge. Here, a computational study has been carried out for the HyShot II scramjet combustor using Large Eddy Simulation (LES) models together with one skeletal and one comprehensive reaction mechanism. Based on a survey of the experimental data available for the HyShot II combustor, we focus on the High Enthalpy Shock Tunnel Göttingen (HEG) operating condition XIII, emulating flight conditions at 28km altitude. To account for slight experimental run-to-run variations, two simulations are performed at different equivalence ratios. The LES are found to capture the experimental wall-pressure and heat-flux data well compared to the measurement data, with marginal influence of the reaction mechanism. The LES results are subsequently used to analyze the flow, mixing, and combustion processes involved. The tools employed include conventional, as well as recently developed methods, such as the Takeno flame index and Chemical Explosive Mode Analysis. These methods give a concise description of the interactions between flow, fuel–air mixing, and combustion, and it is discovered that supersonic combustion is a combination of auto-ignition and non-premixed flame regions and self-igniting fronts. Furthermore, ignition is enabled by shocks, and the supersonic flame is very different in nature to subsonic turbulent flames.