Two-dimensional centered wave flow patches to the Guderley Mach reflection configurations for steady flows in gas dynamics

Abstract

In an attempt to resolve the von Neumann triple point paradox in shock reflection phenomenon, a new type of reflection configuration, called Guderley Mach reflection, was observed both in numerical simulations and physical experiments recently. In this type of reflection configuration, there exists a sequence of triple points, with a centered expansion fan and a supersonic patch at each triple point. In this paper, we present a mathematical analysis of the centered wave flow patches of Guderley Mach reflection. In order to construct such a flow patch, a centered wave problem is introduced. The existence of a global classical solution to the centered wave problem for the two-dimensional isentropic irrotational steady Euler equations is established.