An investigation of the accuracy of high-order methods for hypersonic shock wave turbulent boundary layer interaction (SWTBLI) is presented. The numerical methods considered here comprise of the Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) and Weighted Essentially Non-Oscillatory (WENO) schemes, 2nd to 9th order accurate in conjunction with structured and mixed element unstructured grids. Both Implicit Large Eddy Simulation (ILES) and Reynolds Averaged Navier-Stokes (RANS) computations have been performed. The effects of discretization on the turbulence transport equation, including the approximation method for the viscous gradient, are also investigated. The accuracy of the schemes in high Reynolds number RANS modeling is assessed against experimental data of a shock impingement on a flat plate at Mach number 5 and unit Reynolds number 37×106/m. ILES has been performed for the compression ramp case at moderate Reynolds numbers of 38.7×103, based on the boundary layer thickness, and compared to Direct Numerical Simulations (DNS).