A shock-detecting sensor for filtering of high-order compact finite difference schemes

High-order simulation of flows containing shock waves is an extremely difficult task due to the discontinuous changes in flow properties across the shock. The present work investigates a shock-detecting sensor for filtering of high-order compact finitedifference schemes to examine the shock-capturing in direct simulation of NavierStokes solver. Based on the accuracy and minimum dissipation error, the shockdetecting sensor is selected for the DNS studies. The implementation of high resolution simulations using sixth-order compact schemes with a fourth-order tworegister Runge-Kutta method is validated through selective test problems. Through several numerical experiments (including an inviscid shock/vortex interaction, a viscous shock/vortex interaction, and a shock/mixing layer interaction) the accuracy of the nonlinear filter is examined. The results indicate that the shock-detecting sensor works well, and can be used for future simulations of turbulent flows containing shocks.