The main objective of the present work is to numerically simulate the shock-vortex interactions that arise in the transonic turbulent cross flow, subcritical and supercritical, around a circular cylinder. For doing so, the compressible Navier-Stokes equations are solved by means of a finite-volume discretization. For the flux calculation the skew symmetric Ducrosâ€™ method with 4 th order of accuracy is used. For the marching process the 3 rd order Runge-Kutta method, with modifications as proposed by Shu, is used, giving the methodology 3 rd order of accuracy in time. For the subcritical case (subcritical stands for a type of flow where the boundary layer is laminar up to the separation point) no closure models are used. This was so because the turbulence models assume a fully turbulent, more energetic, boundary layer that would lead to a physically inconsistent delay in the detachment. For the supercritical case (supercritical stands for a type of flow where the boundary layer is turbulent before the separation point) the SST-DES model, as proposed by Strelets, is applied. Such model was chosen because it allies the capability of MenterSST model to capture with accuracy the separation point without the need of an extremely large resolution in the boundary layer region with the LES capability of a very large range of scales in the wake region without over-damping or over-dissipating them. So, firstly, the subsonic subcritical flow around the cylinder, with M=0.2 and Re=90000, is simulated without closure models. This simulation is aimed at validating the no turbulence models approach because such a case has a considerably large amount of experimental results for comparison. Then, the transonic subcritical flow around the cylinder, with M=0.8 and Re=166000, is simulated using no closure models and the transonic supercritical flow around the cylinder, with M=0.8 and Re=500000, is simulated using the SST-DES model proposed by Strelets. The calculated results are then compared with those experimental available in the literature. Then the complex topology present in such a type of flow is analyzed by means of the flow field visualizations that permit seeing the vortices and shock waves that aris |