High-order Shock Capturing Schemes for Turbulence Calculations

The goal of this work is to investigate methods for simulating turbulent supersonic flows that include shock waves. Several different types of previously proposed characteristic filters, including total variation diminishing (TVD), monotone upstream-centered scheme for conservation laws (MUSCL), and weighted essentially non-oscillatory (WENO) filters, are investigated in this study. Similar to the traditional shock capturing schemes, these filters can not only eliminate the numerical instability caused by large gradients in flow fields, but also improve efficiency compared to classical shock-capturing schemes. Adding the nonlinear dissipation part of a classical shock-capturing scheme to a central scheme makes the method suitable for incorporation into any existing central-based high-order subsonic code. The amount of numerical dissipation to add is sensed by means of the artificial compression method (ACM) switch. In order to improve the performance of the characteristic filters, shock sensors are also employed and investigated. Through several numerical experiments (including a shock/density wave interaction, a shock/vortex interaction, and a shock/mixing layer interaction) we show that characteristic filters work well, and can be used for future turbulent flow simulations that include shocks.