Physical/numerical duality of explicit/implicit subgrid-scale modelling

International audience ; The development of implicit approaches has prompted debate on the actual usefulness of any explicit subgrid-scale modelling in large-eddy simulation. This question is addressed here by considering two generic turbulent flows: (i) the Taylor-Green vortex problem; (ii) the pipe flow. For both flow configurations, implicit modelling is found to overtake the very popular Smagorinsky model. To understand this robust observation, an analysis in the Fourier space is presented for the Taylor-Green vortex problem. The concept of spectral eddy viscosity, widely used in the pioneer work of Marcel Lesieur in two-point closure and subgrid-scale modelling, is revisited in a general framework based on explicit/implicit subgrid-scale modelling. In particular, the essentially anisotropic nature of implicit modelling is exhibited, as a favourable feature in terms of consistency with the computational mesh. Smagorinsky's model, considered as a generic explicit subgrid-scale model in the framework of Boussinesq's hypothesis, is found to be highly sensitive to numerical errors. Removing the latter is easy but makes computationally inefficient this type of explicit modelling. Comparisons between a priori and a posteriori spectral eddy viscosities show that neither Smagorinsky's model nor implicit modelling can mimic the expected spectral behaviour. Smagorinsky's model is observed to be weakly scale-selective with a poor ability to actually filter the solution. The feature of scale-selectivity is well replicated by implicit modelling which exhibits excellent capabilities for filtering. However, its lack of influence at large scale is against the expected behaviour for the spectral eddy viscosity at low wavenumber through the establishment of a non-zero plateau value. This lack of consistency of implicit LES could be overcome thanks to an extra explicit modelling but the attempt to mix Smagorinsky's model and implicit LES is not successful in this study. The potential of implicit large-eddy simulation is also ...