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

Abstract

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.

Artificial-neural-network-based nonlinear algebraic models for large-eddy simulation of compressible wall-bounded turbulence

“…2007; Yuan et al. 2022) were proposed and exhibited a reasonable agreement with the filtered DNS (fDNS) data. Furthermore, Wang et al.…”

“…In the early stages, the model coefficients were mostly determined by the experimental and numerical data. Recently, the dynamical versions of these nonlinear algebraic SGS models (Wang et al 2007;Yuan et al 2022) were proposed and exhibited a reasonable agreement with the filtered DNS (fDNS) data. Furthermore, Wang et al (2021b) proposed a dynamic spatial gradient model, which has good performance in both a priori and a posteriori tests in LES of incompressible isotropic turbulence.…”

“…(3.18a-f ) Similar to the DSM, the dimensionless model coefficients 3.11) and (3.17) respectively can also be solved dynamically based on the Germano identity (Germano et al 1991;Lilly 1992;Yuan et al 2022). Therefore, this original dynamic nonlinear algebraic model is named the 'ODNA model' for brevity.…”

“…1991; Lilly 1992; Yuan et al. 2022). Therefore, this original dynamic nonlinear algebraic model is named the ‘ODNA model’ for brevity.…”

“…1991; Lilly 1992; Yuan et al. 2022), the ODNA model cannot achieve a very good performance in a priori tests. Therefore, the dimensionless model coefficients , and in (3.4), (3.11) and (3.17) respectively can also be determined by the ANN method (Xie et al.…”