Numerical Investigation of the Von Neumann Paradox for Weak Shocks Using a Higher Order Discontinuous Galerkin Method and Overset Grids

In this paper, we investigate the Guderley Mach reflection that occurs when a weak shock reflects off a plane wedge numerically using a higher order discontinuous Galerkin method and overset grids. Guderley Reflection (existence of a single supersonic patch near the triple point) and Guderley Mach reflection (existence of multiple supersonic patches near the triple point) are the suggested solutions for the resolution of the von Neumann paradox in the weak shock reflection. We confirm the existence of multiple supersonic patches near the triple point for three different configurations. We observe that refining the grid near the triple point increases the number of supersonic patches that occur and Guderley Mach reflection occurs in each case. We have also observed that the number of supersonic patches further increase if we add viscous fluxes near the triple point. These numerical solutions lend credence to the observation reported in Tesdall et al. (JSC 64:721–744, 2015) that the Guderley reflection is not a distinct reflection geometry and it is only an under resolved Guderley Mach reflection.