The design and off-design studies of the hypersonic air-breathing engines face many challenges, due to the complexity of their internal flows. The mixing and combustion processes in Supersonic-Combustion Ramjet (scramjet) engines involve complicated aerothermochemical features, such as: the interactions between shock-waves and boundary-layer, the shock induced-combustion and the recirculation zones. In this study, a numerical solver is developed and validated to be an efficient design tool capable of simulating these complicated flow features of the supersonic combustors. For the code...