  In a recent paper, Liu et al. [``Lift and drag in three-dimensional steady
viscous and compressible flow'', Phys. Fluids 29, 116105 (2017)] obtained a
universal theory for the aerodynamic force on a body in three-dimensional
steady flow, effective from incompressible all the way to supersonic regimes.
In this theory, the total aerodynamic force can be determined solely with the
vorticity distribution on a single wake plane locating in the steady linear far
field. Despite the vital importance of this result, its validity and
performance in practice has not been investigated yet. In this paper, we
performed Reynolds-averaged Navier-Stokes simulations of subsonic, transonic,
and supersonic flows over a three-dimensional wing. The aerodynamic forces
obtained from the universal force theory are compared with that from the
standard wall-stress integrals. The agreement between these two formulas
confirms for the first time the validity of the theory in three-dimensional
steady viscous and compressible flow. The good performance of the universal
formula is mainly due to the fact that the turbulent viscosity in the wake is
much larger than the molecular viscosity therein, which can reduce
significantly the distance of the steady linear far field from the body. To
further confirm the correctness of the theory, comparisons are made for the
flow structures on the wake plane obtained from the analytical results and
numerical simulations. The underlying physics relevant to the universality of
the theory is explained by identifying different sources of vorticity in the
wake.
