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

Advances in Aerodynamics

Table 4 Correlation coefficients and relative errors of the SGS stress at filter scale \(\bar {\Delta }=32 h_{\text {DNS}}\) in the a priori study

	\(\tau _{11}^{A}\)	\(\tau _{22}^{A}\)	\(\tau _{33}^{A}\)	\(\tau _{12}^{A}\)	\(\tau _{23}^{A}\)	\(\tau _{13}^{A}\)
Model \C(\(\tau _{ij}^{A}\))
DSM	0.294	0.29	0.295	0.325	0.308	0.32
DMM	0.6	0.597	0.596	0.61	0.602	0.609
VGM	0.922	0.921	0.92	0.922	0.921	0.922
ANNSGM-7-49	0.944	0.945	0.944	0.944	0.943	0.942
DNAM-LS	0.927	0.926	0.925	0.927	0.926	0.927
DNAM-GID	0.913	0.913	0.912	0.913	0.913	0.914
DNAM-SSD	0.926	0.925	0.925	0.926	0.925	0.927
Model \ E_r(\(\tau _{ij}^{A}\))
DSM	0.975	0.978	0.977	0.963	0.971	0.964
DMM	0.802	0.804	0.806	0.797	0.803	0.797
VGM	0.405	0.407	0.409	0.405	0.407	0.404
ANNSGM-7-49	0.341	0.342	0.340	0.329	0.335	0.338
DNAM-LS	0.376	0.377	0.379	0.375	0.378	0.374
DNAM-GID	0.479	0.479	0.482	0.483	0.483	0.48
DNAM-SSD	0.38	0.381	0.383	0.379	0.382	0.378