High Order Numerical Methods for LES of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. The high order low dissipative method of Yee & Sjögreen (2009) using adaptive flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems both of these new approaches show a similar accuracy improvement to that of the full use of the SGS terms. One of the numerical accuracy improvements included here applies Harten's subcellre solution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.