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

Advances in Aerodynamics

Table 3 Correlation coefficients and relative errors of the SGS stress at filter scale \(\bar {\Delta }=16 h_{\text {DNS}}\) 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	0.256	0.255	0.24	0.26	0.279	0.253
DMM	0.628	0.617	0.605	0.608	0.624	0.615
VGM	0.952	0.949	0.949	0.947	0.95	0.95
ANNSGM-7-49	0.981	0.980	0.982	0.981	0.981	0.982
DNAM-LS	0.953	0.951	0.951	0.949	0.952	0.952
DNAM-GID	0.942	0.939	0.938	0.936	0.94	0.939
DNAM-SSD	0.952	0.95	0.95	0.948	0.951	0.951
Model \ E_r(\(\tau _{ij}^{A}\))
DSM	0.986	0.99	0.999	0.991	0.979	0.993
DMM	0.779	0.788	0.798	0.796	0.784	0.791
VGM	0.32	0.327	0.327	0.332	0.324	0.323
ANNSGM-7-49	0.199	0.201	0.202	0.197	0.194	0.192
DNAM-LS	0.302	0.309	0.31	0.314	0.307	0.306
DNAM-GID	0.432	0.438	0.442	0.446	0.44	0.439
DNAM-SSD	0.305	0.312	0.313	0.318	0.31	0.309