Comparison of high-order numerical methodologies for the simulation of the supersonic Taylor–Green vortex flow

This work presents a comparison of several high-order numerical methodologies for simulating shock/turbulence interactions based on the supersonic Taylor–Green vortex flow, considering a Reynolds number of 1600 and a Mach number of 1.25. The numerical schemes considered include high-order Finite Difference, Targeted Essentially Non-Oscillatory, Discontinuous Galerkin, and Spectral Difference schemes. The shock capturing methods include high-order filtering, localized artificial diffusivity, non-oscillatory numerical fluxes, and local low-order switching. The ability of the various high-order numerical methodologies to both capture shocks and represent accurately the development of turbulent vortices is assessed.