  We prove convergence of a finite difference approximation of the compressible
Navier--Stokes system towards the strong solution in $R^d,$ $d=2,3,$ for the
adiabatic coefficient $\gamma>1$. Employing the relative energy functional, we
find a convergence rate which is \emph{uniform} in terms of the discretization
parameters for $\gamma \geq d/2$. All results are \emph{unconditional} in the
sense that we have no assumptions on the regularity nor boundedness of the
numerical solution. We also provide numerical experiments to validate the
theoretical convergence rate. To the best of our knowledge this work contains
the first unconditional result on the convergence of a finite difference scheme
for the unsteady compressible Navier--Stokes system in multiple dimensions.
