Time dependent boundary conditions for hyperbolic systems
Journal of Computational Physics
Stable boundary conditions and difference schemas for Navier-Stokes equations
SIAM Journal on Numerical Analysis
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Accurate solutions of the Navier-Stokes equations despite unknown outflow boundary data
Journal of Computational Physics
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Journal of Computational Physics
On flux-extrapolation at supersonic outflow boundaries
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Review of code and solution verification procedures for computational simulation
Journal of Computational Physics
Well-Posed Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
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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.