Dynamic nonlinear algebraic models with scale-similarity dynamic procedure for large-eddy simulation of turbulence

A dynamic nonlinear algebraic model with scale-similarity dynamic procedure (DNAM-SSD) is proposed for subgrid-scale (SGS) stress in large-eddy simulation of turbulence. The model coefficients of the DNAM-SSD model are adaptively calculated through the scale-similarity relation, which greatly simplifies the conventional Germano-identity based dynamic procedure (GID). The a priori study shows that the DNAM-SSD model predicts the SGS stress considerably better than the conventional velocity gradient model (VGM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM) and DNAM-GID model at a variety of filter widths ranging from inertial to viscous ranges. The correlation coefficients of the SGS stress predicted by the DNAM-SSD model can be larger than 95% with the relative errors lower than 30%. In the a posteriori testings of LES, the DNAM-SSD model outperforms the implicit LES (ILES), DSM, DMM and DNAM-GID models without increasing computational costs, which only takes up half the time of the DNAM-GID model. The DNAM-SSD model accurately predicts plenty of turbulent statistics and instantaneous spatial structures in reasonable agreement with the filtered DNS data. These results indicate that the current DNAM-SSD model is attractive for the development of highly accurate SGS models for LES of turbulence.