Self-Similar Solutions for Weak Shock Reflection

Abstract

We present numerical solutions of a two-dimensional Riemann problem for the unsteady transonic small disturbance equations that provides an asymptotic description of the Mach reflection of weak shock waves. We develop a new numerical scheme to solve the equations in self-similar coordinates and use local grid refinement to resolve the solution in the reflection region. The solutions contain a remarkably complex structure: there is a sequence of triple points and tiny supersonic patches immediately behind the leading triple point that is formed by the reflection of weak shocks and expansion waves between the sonic line and the Mach shock. An expansion fan originates at each triple point, thus resolving the von Neumann paradox of weak shock reflection. These numerical solutions raise the question of whether there is an infinite sequence of triple points in an inviscid weak shock Mach reflection.