High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks (Communications in Computational Physics, 2018)
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 addressesthe accuracy improvement of LES of turbulent flows in two ways: (a) from theSGS model standpoint and (b) from the numerical method improvement standpoint.In an internal report, Kotov et al. ("High Order Numerical Methods for large eddysimulation (LES) of Turbulent Flows with Shocks", CTR Tech Brief, Oct. 2014, StanfordUniversity), we performed a preliminary comparative study of different approachesto reduce the loss of accuracy within the framework of the dynamic Germano SGSmodel. The high order low dissipative method of Yee & Sjögreen (2009) using localflow sensors to control the amount of numerical dissipation where needed is used forthe LES simulation. The considered improved dynamics model approaches includeapplying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disablingthe SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interactionproblems, both of these approaches show a similar accuracy improvement tothat of the full use of the SGS terms. The present study focuses on a five levels of gridrefinement study to obtain the reference direct numerical simulation (DNS) solutionfor additional LES SGS comparison and approaches. One of the numerical accuracyimprovements included here applies Harten's subcell resolution procedure to locateand sharpen the shock, and uses a one-sided test filter at the grid points adjacent to theexact shock location.