To design the next-generation aircraft and engines, efficient numerical tools need to be developed. Shock wave/boundary layer interactions are indeed putting the current industrial methods to the test: high-order methods lack robustness while modeling assumptions in low-fidelity methods make them not accurate enough. This work presents the first steps toward improving turbulence modeling in harmonic methods for shock-induced separated flows in turbomachinery applications, using high-fidelity data. A high-order solver based on the flux reconstruction framework is employed for performing high-fidelity simulations. Robustness is ensured by an enhanced artificial viscosity, allowing to capture shocks while not damping turbulence. A canonical oblique shock wave/boundary layer is first investigated to validate the solver and the results are in excellent agreement with the abundant existing literature. Then, the periodically forced transonic flow over a bump is considered. A study of the sensitivity to the perturbation frequency is carried out and highlights different flow regimes. The performance of the harmonic method for the bump case is finally shown to be inferior compared to the unsteady results. As a future step, the high-fidelity data generated will help to reduce the gap between the two.