A finite volume/element discretization on tetrahedral meshes of the variation- al multiscale formulation of large eddy simulations is proposed for turbulent compressible flows. This discretization features an economical procedure based on agglomeration for separating a priori the scales, a corresponding projector for eliminating the small scales from the system of equations, and an effective control of the numerical dissipation induced by upwinding. The resulting LES method is validated with the three-dimensional numerical simulation of a low-speed flow past a square cylinder at M_¥ = 0.1 and Re = 22,000, and various comparisons with experimental data.