A numerical method for the self-similar hypersonic viscous shear layer (Q811251)

As an example for the treatment of a ``hypersonic strong viscous interaction'' in the presence of a large surface mass injection a hypersonic laminar boundary-layer flow in the limiting case of the outer Mach number tending to infinity is discussed in the approximative form of a self-similar solution. Therefore adopting the nondimensional streamwise coordinate and the stream function as independent variables and a reduced temperature and flow velocity as dependent ones, the governing partial differential equations of boundary-layer type are replaced by a system of ordinary differential equations. The arising two-point boundary-value problem is solved on the one hand with the help of asymptotic series expansions which are needed to fulfill the boundary conditions on one side of the boundary-layer and on the other hand by a numerical method. This method is discussed in detail. Several possibilities are mentioned in connection of this and finally a special continuation method is adopted utilizing a Newton-based second- order finite difference scheme and a nonuniform computational grid. This numerical procedure appears to offer a useful general technique which can replace the asymptotic boundary conditions mentioned above.