High accuracy schemes for compressible turbulence simulations

The study of high accuracy numerical schemes is a hot topic for decades in the field of compressible turbulence simulations. Linear compact schemes, high-order shock-capturing schemes and the hybrid schemes are three types of schemes used in today's turbulent flow simulations. The fifth-order compact scheme, WENO scheme and hybrid compact-WENO scheme are introduced as the representatives of these three types of schemes. The high Reynolds number Taylor-Green vortex simulation is used as a typical test of turbulence simulations. The results of the three schemes are compared. In addition, the numerical dissipation are separated from the total dissipation and the numerical resolution property of the schemes are further analyzed. Results demonstrate that the linear compact scheme has the best resolution property for the shock-free flows. The hybrid scheme shows advantages in balancing numerical dissipation and dispersion errors, so they are suitable for under-resolved turbulence simulations even though the flow is free of shocks.