Density-unweighted subgrid-scale models for large-eddy simulations of compressible turbulence

Abstract

Density-unweighted methods in large-eddy simulations (LES) of turbulence have received little attention, and the modeling of unclosed terms using density-unweighted methods even less. We investigate the density-unweighted subgrid-scale (SGS) closure problem for LES of decaying compressible isotropic turbulence at initial turbulent Mach numbers 0.4 and 0.8. Compared to the LES with Favre (density-weighted) filtering, there are more unclosed SGS terms for density-unweighted LES, which can be reconstructed using different SGS models, including the gradient model (GM), approximate deconvolution model (ADM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the dynamic iterative approximate deconvolution (DIAD) models proposed by Yuan et al. “Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence,” Phys. Fluids 33, 085125 (2021). We derive GM models suitable for density-unweighted methods. We also, for the first time, apply the DIAD model to investigate compressible turbulence. In the a priori tests, the correlation coefficients of the GM, ADM, and DIAD models are larger than 0.9. Particularly, the correlation coefficients of DIAD models exceed 0.98 and the relative errors are below 0.2, which is superior to that in other SGS models. In the a posteriori tests of the density-unweighted LES, the DIAD model shows great advantages over other SGS models (including GM, ADM, DSM, and DMM models) in predicting the various statistics and structures of compressible turbulence, including the velocity spectrum, probability density functions (PDFs) of SGS fluxes and the instantaneous spatial structures of SGS heat flux, SGS kinetic energy flux, and vorticity.