The boundary-layer separation and subsequent reattachment due to the free shear-layer and Shockwave interaction have a significant impact on the aerothermal design of supersonic aerospace systems. This problem is prevalent in high-speed flights and can significantly affect the skin friction, aerodynamic loads, and heat transfer. In recent years, considerable progress has been achieved in the prediction of turbulent compressible flows using high-fidelity models. However, the prediction of reattaching free shear-layer and shockwave interactions still needs to be modified for accurate predictivity. The objective of this study is to investigate the ability of a new computational fluid dynamics model to predict these critical flow phenomena accurately. The new high-fidelity model is based on a collocated central scheme, which has the advantage of being a Riemann free solver, and therefore easy to implement on unstructured grids. It is developed to capture any discontinuities at shocks while it is able to capture broadband spatial and temporal variations in turbulent flows with minimal dissipation and dispersion. Large Eddy Simulation is performed on a compression corner at a Mach number of 2.92 and a high Reynolds number. The geometry of the model is specifically designed to isolate the reattachment process of a high-speed separated flow. To examine the accuracy of the predicted results, results of velocity profiles in the free shear-layer, boundary layer development, turbulent fluctuations, and pressure are compared to an experimental effort by Princeton. Excellent agreement is observed, and it is recommended that the model can be used to investigate the physics of the shock unsteadiness due to interaction with a free shear-layer.