Comparison of DNS and LES of transitional and turbulent compressible flow: flat plate and mixing layer

We present a priori and a posteriori test results of LES (large eddy simulation) of compressible flow over a flat plate and in a mixing layer. Through a comparison with filtered DNS (direct numerical simulation) data the 'quality' of subgrid-models for the turbulent stress can be assessed. In particular, the scale similarity model of Bardina and the dynamic mixed model arising from a combination of Bardina's model with the Germano eddy-viscosity model show excellent correlations a priori, and give rise to accurate LES simulations a posteriori. Moreover, the filtering approach close to solid walls is considered and the contribution to the filtered equations arising from the non-commutation of the filter operator with the partial derivatives is calculated. It appears, in a priori tests for 2D simulations, that these non-commutation terms can be comparable to the turbulent stress. The scale similarity hypothesis yields models for these terms which show a good correlation.