An implicit finite-difference method is used to study the interaction of a laminar boundary layer with a supersonic, external, inviscid flow on a flat plate with a sharp or rounded backward facing step. The boundary-layer equations are used to describe the subsonic portion of the flow with the effect of transverse pressure gradients in the supersonic viscous region included through the use of an inviscid transverse momentum equation. Initial profiles are assumed to be similar (Blasius) in shape, but with the boundary-layer edge flow inclination not specified. The qualitative nature of the downstream flow is determined by the particular value of initial edge flow inclination chosen, with two families of solutions bounded by a particular solution which continues downstream on the body without separation. A perturbation in the initial edge flow inclination from this particular value results in a flowfield such as one would expect approaching a sharp backward facing step. A perturbation in the opposite direction results in a flowfield such as one would expect for a boundary layer separating from a smooth wall in an adverse pressure gradient. Computed wall pressure distributions agree well with experiments for both sharp and rounded corners and the computed flowfield for a rounded corner contains a separation shock whose location also agrees with experiment.
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