Abstract : The present AFOSR project focuses on the theoretical modeling and numerical simulation of liquid-propellant rocket engine injector flow and combustion dynamics. Emphasis is placed on cryogenic propellants in both shear and swirl co-axial injectors at supercritical conditions. The formulation is based on the full conservation equations in three dimensions, and accommodates variable properties and finite-rate chemical kinetics. Full account is taken of various high-pressure phenomena such as thermodynamic non- idealities and transport anomalies commonly observed in the transcritical regime. Furthermore, an efficient numerical framework utilizing state-of-the-art computer software and hardware technologies is implemented, such that sweeping calculations can be conducted within a realistic time frame. Various fundamental physiochemical mechanisms associated with cryogenic propellant injection, mixing, and combustion are studied systematically. Results have not only enhanced basic understanding of the subject problem, but also established a quantitative basis to identify and prioritize the key design parameters and flow variables that exert strong influences on the injector behavior in different environments.