A Study of Shock Capturing Methods for Simulations of Compressible Turbulence with Shock Waves

Turbulence and shock waves interactions occur in a wide range of applications, such as mixing, flow separation and combustion. However, it is still a challenge to accurately simulate these problems. The two demands seem contradictory: the simulation of small turbulence scales requires non-dissipative scheme while the capture of shock requires dissipative scheme. We evaluate the performance of several shock capturing methods for this problem with a suite of test cases: Taylor-Green vortex, Shu-Osher problem and compressible isotropic turbulence. The results show that the widely used high order methods and WENO schemes can only satisfy the two demands above to some extent. And the shock capturing methods still need to be improved for the high fidelity simulation of compressible turbulence.