A large-eddy simulation (LES) of a supersonic turbulent boundary layer over a compression ramp is performed using a high-order compact differencing scheme with localized artificial diffusivity (LAD) for shock capturing. The free stream Mach number is M∞ = 2.9, Reynolds number Reθ = 2300, and ramp angle is 24°. An artificial shear viscosity model is used to represent the effects of unresolved sub-grid scales (SGS). The scheme is validated by simulating a two-dimensional laminar shock-boundary layer interaction (SBLI) and comparisoning with experimental and computational results at matching conditions. We further validate our numerical approach for the three-dimensional turbulent compression ramp STBLI to establish further confidence in the ability of the numerical method to accurately predict complex compressible turbulent flow phenomena in the presence of shocks. The analysis focuses on the investigation of flow physics with an emphasis on the low-frequency motion of the shock and separation bubble as observed by previous experimental and computational investigations. Results from the turbulent case are compared against both experimental and direct numerical simulation (DNS) results at matching conditions. The present LES results show good agreement with both the experimental and DNS data. Analysis of the low-frequency unsteady motions indicate a strong connection between the motion of the shock and the size of the separation bubble in both streamwise and wall-normal extents. Low-frequency fluctuations of streamwise velocity are greatest in the region of the shear layer which supports the theory that the low-frequency unsteadiness of the shock is driven by characteristic time scale associated with the entrainment of mass from the shear layer.