High Order Schemes for Shock Capturing

In this chapter, a series of high order shock capturing schemes including WENO scheme, weighted compact scheme, modified upwinding compact scheme are introduced, which can get sharp shock capturing but keep high order accuracy in the smooth area. These schemes are particularly useful for LES of shock-turbulence interaction where both high resolution and sharp shock capturing are important. All these schemes are somehow successful in high order LES for SBLI. An efficient shock detector is introduced as a part of weighted compact and modified upwinding schemes. In addition, the accuracy, truncation errors, dissipation and dispersion of these schemes are analyzed.

Keywords: Compact scheme, Dispersion, Dissipation, High order scheme, Shock capturing, Shock detector, Truncation error, Upwinding scheme, WENO.