This work aims at studying the effects of a low-pressure Argon discharge (P = 0.5 Torr) on a supersonic Argon flow (M = 2) around a flat plate. The observed phenomena during high speed-flow control with a plasma discharge are exhaustively described. The present investigation is of great interest not only to aviation but also to numerous other areas like the wind power industry. The computations have been carried out using the DC discharge and the High Mach Number Flow Comsol Multiphysics modules. To simulate the DC discharge, chemical reactions near the cathode region along with their corresponding Townsend coefficients need to be defined. The latter are calculated using the Bolsig + computer code. The other reactions cross sections are imported from the LXCAT data base. The imported data are used to calculate the reactions rates. The plasma discharge effects on the rarefied supersonic flow are described using a 2D hydrodynamical model under the Drift-Diffusion approximation. The hydrodynamical model was validated by comparing its results for a supersonic air flow with experiments. The main results on an Argon supersonic flow coupled to an Argon discharge show an increase in the pitot pressure and the shock angle.