A modified optimal LES model for highly compressible isotropic turbulence*

An energy budget analysis and a posteriori tests of subgrid-scale (SGS) models for large eddy simulation (LES) of stationary highly compressible homogeneous isotropic turbulence are carried out at M_t ranging from 0.4 to 1.0 and Re_λ ranging from 180 to 250. An energy budget analysis shows that the SGS stress τ_ij and the SGS heat flux Q_j are dominant terms in the current M_t and Re_λ ranges, while other terms can be neglected in LES. We perform LES of compressible isotropic turbulence by using several SGS models including a DSM, a DMM, and an optimal model. In addition, a modified optimal model is constructed based on the magnitude of the filtered strain-rate tensor, inspired by the physical insight that the region of the large magnitude of the filtered strain-rate tensor plays a significant role in kinetic energy transfer. Spectra, statistics, and scaling of velocity and thermodynamic variables from LES are tested. The modified optimal model performs better than other models, especially for the spectrum of the compressible velocity component at relatively low M_t and high Re_λ.