Large-Eddy Simulation (LES); jet phenomena; simulation conditions for cryogenic fluid jet dynamics; most amplified frequency of initial shear layer instability at different pressures; dynamics of simplex swirl injector; geometric parameters and mass flow rate of simplex swirl injector; effect of injector geometry and flow conditions on LOX fluid film thickness and spray cone angle; simulation conditions for analysis of supercritical LOX/methane injection and mixing process