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

Advances in Aerodynamics

Table 2 Correlation coefficients \(C(\mathbb {T}^{(n),A}_{ij}, \tau _{ij}^{A})\) with the increasing of the filter scales

\(\bar {\Delta }/h_{\text {DNS}}\)	\(\mathbb {T}^{(1)}_{11}\)	\(\mathbb {T}^{(2)}_{11}\)	\(\mathbb {T}^{(3)}_{11}\)	\(\mathbb {T}^{(4)}_{11}\)	\(\mathbb {T}^{(5)}_{11}\)	\(\mathbb {T}^{(1)}_{12}\)	\(\mathbb {T}^{(2)}_{12}\)	\(\mathbb {T}^{(3)}_{12}\)	\(\mathbb {T}^{(4)}_{12}\)	\(\mathbb {T}^{(5)}_{12}\)
2	0.227	0.44	0.518	0.824	0.549	0.219	0.429	0.513	0.819	0.545
4	0.227	0.425	0.519	0.821	0.534	0.221	0.415	0.514	0.816	0.529
8	0.233	0.401	0.513	0.808	0.509	0.228	0.394	0.509	0.804	0.5
16	0.256	0.384	0.498	0.789	0.488	0.253	0.38	0.498	0.781	0.468
32	0.3	0.385	0.487	0.777	0.491	0.306	0.389	0.493	0.755	0.448
64	0.334	0.398	0.498	0.788	0.535	0.384	0.431	0.508	0.737	0.464