Self-similar solutions for the diffraction of weak shocks

We numerically solve a problem for the unsteady transonic small disturbance equations that describes the diffraction of a weak shock into an expansion wave. In the context of a shock moving into a semi-infinite wall, this problem describes the interaction between the reflected part of the shock and the part that is transmitted beyond the wall. We formulate the equations in self-similar variables, and obtain numerical solutions using high resolution finite difference schemes. Our solutions appear to show that the shock dies out at the sonic line, rather than forms at an interior point of the supersonic region.

► We numerically study an asymptotic problem that describes the diffraction of a weak shock into an expansion wave.
► We solve this problem in self-similar coordinates using a high-resolution finite difference scheme.
► The solution appears to show that the shock disappears on the sonic line, which differs from solutions for shock formation in steady and self-similar flow which show that the shock typically forms inside the supersonic region.