Staged transverse sonic injection into supersonic flow in a confined environment usually employed in scramjet combustor has been explored numerically using an indigenously developed three-dimensional Reynolds Averaged Navier Stokes solver with Roes scheme and k-w turbulence model. Simulations were carried out for both without injection and with injection in Mach 2 flow behind a backward-facing step in a rectangular duct. Simulation captured all finer details of flow structures including recirculation bubble behind a backward-facing step, barrel shocks and Mach discs caused due to transverse injection and reattachment of shear layer in the downstream wake region. K-w turbulence model with compressibility correction performed extremely well in predicting the overall behaviour of the flow field. The jet from the second injector was found to penetrate more in the free-stream due to the loss of free-stream total pressure across the barrel shock of the first injection point. Excellent agreement of computed profiles of various flow parameters at different axial locations in the duct with experimental results and other numerical results available in the literature demonstrate the robustness and accuracy of the indigenously developed code.