Simulations of spatially evolving compressible turbulence using a local dynamic subgrid model

A new dynamic model for large eddy simulations (LES) of compressible turbulent flows has been developed. It allows the model coefficients to be calculated in a localized fashion. The properties of the model have been examined in LES of decaying isotropic turbulence for a range of Mach numbers and Reynolds numbers. In the limit as Mach number approaches zero, the model reduces to an appropriate incompressible form. In the compressible regime, the results agree closely with data from comparable direct simulations. For a fully developed turbulent flow field, the modelled subgrid stress tensor was found to satisfy all of the realizability conditions over a vast majority of the domain. The model was then applied to LES of high Reynolds number spatial mixing layers. It was determined that in order to obtain good results for such a case, the numerical scheme must be minimally dissipative. Otherwise, the physics of the flow, specifically the viscous and turbulent stresses, were overwhelmed by the numerical dissipation of the scheme, resulting in a greatly decreased mixing layer growth rate. Therefore a scheme was developed which has very little inherent dissipation. Even with a relatively coarse and highly stretched grid, the results from this scheme were in good agreement with experimental data.