Numerical solution of the problem of unsteady supersonic flow around the front part of the wings with a detached shock wave

The object of this paper is to describe a numerical method for the solution of the problem of unsteady supersonic flow around the front part of the wings with a detached shock wave. The planform and the airfoil of the wings must be constructible but otherwise arbitrary. The velocity vector of the free stream is directed in an arbitrary direction but without flow separation. The problem is formulated for the three-dimensional, hyperbolic system of equations of unsteady, inviscid, chemically reactive gas flow in a mixed subsonic and supersonic domain. It is solved by a finite difference, implicit, second-order method with the use of the time-dependent stationing principle. A curvilinear coordinate system is introduced in which the numerical domain becomes a simple rectangle. The coordinate system is time-dependent and adapted for the planform of the wing and the free-stream parameters. The planform of the wind and the velocity vector of the free stream may be changed in the time-dependent stationing process. The flow field is computed around the front part of wings which have an elliptical planform and an aspect ratio λ ⩽ 2 for selected values of M æ between 1.5 and 5.