High Order Numerical Methods for the Dynamic SGS Model 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.
In an internal report, Kotov et al. ( ”High Order Numerical Methods for large eddy
simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford
University), we performed a preliminary comparative study of different approaches
to reduce the loss of accuracy within the framework of the dynamic Germano SGS
model. The high order low dissipative method of Yee & Sj ¨ogreen (2009) using local
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 approaches show a similar accuracy improvement to
that of the full use of the SGS terms. The present study focuses on a five levels of grid
refinement study to obtain the reference direct numerical simulation (DNS) solution
for additional LES SGS comparison and approaches. One of the numerical accuracy
improvements included here applies Harten’s subcell resolution procedure to locate
and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the
exact shock location.
