Large-eddy simulation (LES) of an oblique shock impinging on a supersonic turbulent boundary layer is carried out with a high-order compact differencing scheme using localized artificial diffusivity (LAD) for shock capturing. Flow conditions attempt to match those of the tomographic particle image velocimetry (PIV) experiments conducted at the Delft University of Technology (M ∞ = 2.05 and φ = 8°). However, due to computational cost, the Reynolds number is taken to be Reδ = 20,000 (1/30th of the experimental Reynolds number), and an attempt is made to geometrically match the interaction parameters. Inflow conditions are generated by an improved recycling/rescaling method to eliminate the non-physical "tones" associated with standard recycling/rescaling. The numerical scheme is first validated by simulating a two-dimensional laminar shock wave / boundary layer interaction (SWBLI). Next, a three-dimensional simulation with progressive mesh refinement is conducted to investigate flow physics and establish confidence in the ability of the computational method to accurately and efficiently simulate complex supersonic flow phenomena. Mean and fluctuating profiles of velocity, pressure, and skin friction provide good indication of grid convergence between the two highest levels of refinement. Instantaneous data fields are analyzed, and observations are made regarding "flapping" motion caused by boundary layer turbulence and spanwise variation in shock location. Additionally, the range of spatial and temporal scales captured by the present work is quantified by analyzing spanwise wavenumber and frequency spectra at various locations in the flow. Through analysis of the frequency spectra of the wall pressure signal, low-frequency motion of the separation bubble with a time scale ∼O(100δ/u ∞) is observed and described. Through direct comparison, we additionally observe that standard recycling/rescaling inflow conditions may result in different low-frequency behavior.