A Non-Linear SGS Model Based On The Spatial Velocity Increment

Abstract

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u i . The new model is inspired by the structure function formulation developed by Metais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ ij and the velocity increment tensor Q ij = δ u i δ u j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re τ = 520 and LES of round turbulent jet at Re D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.