On the outflow conditions for spectral solution of the viscous blunt-body problem

The purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic/hypersonic flow over blunt bodies, governed by the compressible Navier-Stokes equations, with an emphasis motivated primarily by the use of spectral methods without any filtering. The subsonic/supersonic composition of the outflow boundary requires a dual boundary treatment for well-posedness. All compatibility relations, modified to undertake the hyperbolic/parabolic behaviour of the governing equations, are used for the supersonic part of the outflow. Regarding the unknown downstream information in the subsonic region, different subsonic outflow conditions in the sense of the viscous blunt-body problem are examined. A verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution. Detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations. Numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer. It is demonstrated that two approaches for imposing subsonic outflow conditions namely (1) extrapolating all flow variables and (2) extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high-speed flows over blunt bodies using spectral collocation methods.