A high-order low dissipative numerical framework is discussed to tackle simultaneously the modeling of unresolved sub-grid scale flow turbulence and the capturing of shock waves. The flows around two different airfoil profiles are simulated using a Spectral Difference discretisation scheme. First, a transitional, almost incompressible, low Reynolds number flow over a Selig-Donovan 7003 airfoil. Second, a high Reynolds number flow over a RAE2822 airfoil under transonic conditions. These flows feature both laminar and turbulent flow physics and are thus particularly challenging for turbulence sub-grid scale modeling. The accuracy of the recently developed Spectral Element Dynamic Model, specifically capable of detecting spatial under-resolution in high-order flow simulations, is evaluated. Concerning the test in transonic conditions, the additional complexity due to the presence of shock waves has been handled using an artificial viscosity shock-capturing technique based on bulk viscosity. To mitigate the impact of the shock-capturing on turbulence dissipation, it was necessary to combine the high-order modal-type shock detection with a usual sensor measuring the local flow compressibility.
