We numerically integrate the compressible Navier-Stokes equations by m
eans of a finite volume technique on the domain exterior to an airfoil
. The curvilinear grid se use for discretization of the Navier-Stokes
equations is obviously finite, it covers only a certain bounded region
around the airfoil, consequently, we need to set some artificial boun
dary conditions at the external boundary of this region. The artificia
l boundary conditions we use here are nonlocal in space. They are cons
tructed specifically for the case of a steady-state solution. In const
ructing the artificial boundary conditions, we linearize the Navier-St
okes equations around the far-field solution and apply the difference
potentials method. The resulting global conditions are implemented tog
ether with a pseudotime multigrid iteration procedure for achieving th
e steadystate. The main goal of this paper is to describe the numerica
l procedure itself, therefore, we primarily emphasize the computation
of artificial boundary conditions end the combined usage of these arti
ficial boundary conditions and the original algorithm for integrating
the Navier-Stokes equations. The underlying theory that justifies the
proposed numerical techniques will accordingly be addressed more brief
ly. We also present some results of computational experiments that sho
w that for the different flow regimes (subcritical and supercritical,
laminar and turbulent), as well as for the different geometries (i.e.,
different airfoils), the global artificial boundary conditions appear
to be essentially more robust, i.e., they may provide far better conv
ergence properties and much weaker dependence of the solution on the s
ize of computational domain than standard external boundary conditions
, which are usually based on extrapolation of physical and/or characte
ristic variables.