Numerical simulations of von Neumann reflections

The reflection of weak shocks constitutes a challenging problem from a modelling and numerical point of view. Indeed, there exist certain combinations of free-stream Mach number and flow deflection angle for which the Von Neumann theory admits no solution. However, numerical solutions for these same flow parameters show a flow pattern which is very similar to the von Neumann's triple point solution. This inconsistency is referred to as the von Neumann paradox, and the observed reflection pattern is called the von Neumann reflection. In the paper these issues will be investigated by computing von Neumann reflections using different computational approaches including an unstructured shock-fitting technique.