This work uses high‐order discontinuous Galerkin discretization techniques to simulate transitional and turbulent flows through medical devices. Flows through medical devices are characterized by moderate Reynolds numbers and typically involve different flow regimes such as laminar, transitional, and turbulent flows. Previous studies for the FDA benchmark nozzle model revealed limitations of Reynolds‐averaged Navier‐Stokes turbulence models when applied to more complex flow scenarios. Recent works based on large‐eddy simulation approaches indicate that these limitations can be overcome but also highlight potential limitations due to a high sensitivity with respect to numerical parameters. The methodology presented in this work introduces two novel ingredients compared with previous studies. Firstly, we use high‐order discontinuous Galerkin methods for discretization in space. The inherent dissipation and dispersion properties of high‐order discontinuous Galerkin discretizations are expected to render this approach well suited for transitional and turbulent flow simulations. Secondly, to mimic blinded CFD studies, we propose to use a precursor simulation approach in order to predict the inflow boundary condition for laminar, transitional, and turbulent flow regimes instead of prescribing analytical velocity profiles at the inflow. We investigate the whole range of Reynolds numbers as suggested by the FDA benchmark nozzle problem and compare the numerical results to experimental data obtained by particle image velocimetry in order to critically assess the predictive capabilities of the solver on the one hand and the suitability of the FDA nozzle problem as a benchmark in computational fluid dynamics on the other hand.