An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence (Communications in Computational Physics, 2020)
In this paper, the detailed dynamic characteristics of the subgrid scale (SGS)stress tensor and heat flux are investigated through Taylor series expansion in numerical simulations of compressible isotropic turbulence. A new approximate second-orderclosure (ASOC) model is introduced based on the transport equations of the first-orderTaylor series approximation of SGS stress tensor and heat flux. The proposed modelis implemented in large eddy simulation (LES) of compressible isotropic turbulence.Detailed comparisons with direct numerical simulation (DNS) dataset using both apriori and a posteriori approaches are carried out. A priori tests show that, SGS stresstensor and heat flux have high correlations with the first-order Taylor series approximation. Their root mean square (rms) values are close to those of the first-order Taylor series approximation. In a posteriori tests, the proposed ASOC model yields goodagreement with DNS dataset. Compared with the results of the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM), the ASOC model predicts better energy spectra at high wavenumbers. The probability density function (PDF) andthe structure functions of velocity and thermodynamic variables are further studied,demonstrating that the statistical properties of the simulated flows are improved bythe ASOC model. The numerical results illustrate the ability of the model to improvethe statistical properties of the simulated flows in the context of LES. Finally, a simplified ASOC model can be derived by neglecting the effect of density gradient for lowturbulent Mach number turbulence.
Keywords: Compressible turbulence; large eddy simulation; Taylor series expansion; approximate second-order closure model.