EXTERNAL FLOW COMPUTATIONS USING GLOBAL BOUNDARY-CONDITIONS

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.