Direct Numerical Simulation and Implicit Large‐Eddy Simulation of Shock Train in Channel Flow Using High Order Optimised Targeted Essentially Non‐Oscillatory Schemes

ABSTRACT Direct numerical simulation (DNS) and implicit large‐eddy simulation (LES) of turbulent channel flows with isothermal walls, with and without shock trains, are performed using a recently proposed high‐order optimized targeted essentially non‐oscillatory (TENO) scheme. Mean flow and turbulence statistics are presented and compared with those previously obtained from DNS using a bandwidth‐optimized weighted essentially non‐oscillatory (WENO) scheme with limiter. It is observed that the TENO scheme performs better than the WENO scheme in predicting the mean flow and Reynolds stresses in these flows. The optimized TENO scheme used here is found to be very suitable for performing implicit LES on a relatively coarse grid.