This thesis is about on a stabilization technique for the compressible Euler equations with application in the atmospherical flow dynamics. Despite the computational resources available, a Direct Numerical Simulation (DNS) in the atmospherical flow simulations is still far away from our possibilities, this is not only due to the mesh size requirement in terms of storage and computational power, but this is also due to the restriction of the time step in order to respect the CFL condition. One of the remedy of this issue is the LES (Large-eddy-simulation) which is a technique that consists to simulate the large structures while the smallest are modelled by a "sub-grid model".