This paper presents a variational multiscale stabilization for the finite element numerical solution of the Euler and Navier-Stokes equations of compressible flow. All the components of the dual operator are considered in the stabilization term and two options are proposed for the computation of the variational multiscale stabilization subscale. The first option that we call diagonal τ subscale, presents the classical form for the subscale as the product of a parameter τ times the residual of the equation. The second option that we call Fourier subscale uses the Fourier transform in order to model the subscale. We compare these two options for the variational multiscale stabilization subscale through several two-dimensional benchmark cases of different complexity in viscous and inviscid flows, covering a wide range of Mach numbers
