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