On the Self-similar Diffraction of a Weak Shock into an Expansion Wavefront

Abstract

We study an asymptotic problem that describes the diffraction of a weak, self-similar shock near a point where its shock strength approaches zero and the shock turns continuously into an expansion wavefront. An example arises in the reflection of a weak shock off a semi-infinite screen. The asymptotic problem consists of the unsteady transonic small disturbance equation with suitable matching conditions. We obtain numerical solutions of this problem, which show that the shock diffracts nonlinearly into the expansion region. We also solve numerically a related half-space problem with a “soft” boundary, which shows a complex reflection pattern similar to one that occurs in the Guderley Mach reflection of weak shocks.