A priori analyses of three subgrid-scale models for one-parameter families of filters

Abstract

The decay of isotropic turbulence in a compressible flow is examined by direct numerical simulation (DNS). A priori analyses of the DNS data are then performed to evaluate three subgrid-scale (SGS) models for large-eddy simulation (LES): an eddy-diffusivity model (M1) [J. Fluid Mech. 238, 1 (1992)], a stress-similarity model (M2) [J. Fluid Mech. 275, 83 (1994)], and a gradient model (M3) [Theor. Comput. Fluid Dyn. 8, 309 (1996)]. The models exploit one-parameter second- or fourth-order filters of the Pade type, which permit the cutoff wave number kc to be tuned independently of the grid increment Δx. The modeled (M) and exact (E) SGS-stresses are compared component-wise by correlation coefficients of the form C(E,M) computed over the entire three-dimensional fields. In general, M1 correlates poorly against exact stresses (C<0.2), M3 correlates moderately well (C≈0.6), and M2 correlates remarkably well (0.8<C<1.0). Specifically, correlations C(E,M2) are high provided the grid and test filters are of the same order. Moreover, the highest correlations (C≈1.0) result whenever the grid and test filters are identical (in both order and cutoff). Finally, present results reveal the exact SGS stresses obtained by grid filters of differing orders to be only moderately well correlated. This implies for LES that the model cannot be specified independently of the filter.