Subfilter-Scale Stress Modelling

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Personnel: Prof. Ugo Piomelli, Dr. Oriol Lehmkuhl (Barcelona Supercomputing Centre), Mr. Zvi Hantsis, Mr. Francesco Ambrogi
BFS grid

Figure 1. Grid size and arrangement for the backward-facing step (BFS) calculations; 256×100×64 points. 

BFS eddy viscosity
Figure 2. SFS eddy-viscosity in the BFS using 256×100×64 grid points. (a) Dynamic model. (b) Local ILSA  

A critical feature of large-eddy simulations (LES) is the definition of the filter width Δ, which represents the smallest scale resolved in the calculation, and is the length-scale typical of the unresolved eddies.  To satisfy the basic assumption of LES, this filter-width should be a fraction of the integral length scale, representative of the eddies that dominate mixing and momentum transport, and must be resolved. In most existing LES, on the other hand, the filter width is related to the local grid size. Calculations of complex flows, however, require computational meshes refined only in regions where higher resolution is required.  The grid may be discontinuous, and the classical modelling approach for LES gives unphysical results. This issue and related ones are discussed in depth in [1].  We have developed an alternative approach in which the physics of turbulence themselves dictate the model length scale.  The filter width Δ is decoupled from the computational grid, being rather a measure of the local integral scale of the flow that can be estimated from the turbulent kinetic energy and dissipation. We considered various measures of the activity of the unresolved scales mentioned in the literature and proposed a new one, more consistently applicable to high-Re flows. This model (the Integral Length-Scale Approximation—ILSA—model) has given very promising results when applied to canonical flows [1].

A modification of this model has recently been developed [5]. First, we define a new measure of subfilter-scale (SFS) activity (based on turbulent stresses), which adds to the robustness of the model, particularly at high Reynolds numbers. This modification has the added benefit that no prior calculations are required, and the model coefficient can be calculated dynamically during the calculation, adapting to large-scale unsteadiness. Furthermore, the SFS activity is now enfored locally (and not integrated over the entire volume, as in the original model). The local assignment of SFS activity provides a better control over model activity, and also significantly improved near-wall behaviour of the model. Application of local ILSA to channel flow and backward-facing step, and comparison with the original ILSA and with the dynamic model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] shows the better control over the model contribution in local ILSA, while the positive properties as the original formulation (including its higher accuracy compared to the dynamic model on coarse grids) are maintained. The backward facing step also highlights the advantage of the decoupling of the model length scale from the mesh.  While, with the dynamics model, the eddy viscosity becomes small in regions of grid refinement (Figures 1 and 2a), with the local ILSA model a continuous distribution of the eddy viscosity is obtained (Figure 2b).  This characteristic better reflects the physics of the flow, which are dominated by advection; a locally small value of the eddy viscosity does not reflect the contribution of SFS eddies advected from upstream, whose scale is determined by their history, and not by the local mesh.

Sponsors: NSERC.


  1. U. Piomelli, A. Rouhi, and B. J. Geurts. A grid- independent length scale for large-eddy simulations. J. Fluid Mech., 766:499–527, 2015.
  2. A. Rouhi, U. Piomelli, and P. Vlachos. Numerical investigation of pulsatile flow in endovascular stents. Phys. Fluids25:091905-1-18, 2013.
  3. A. Rouhi, U. Piomelli, and B. J. Geurts. A dynamic subfilter-scale stress model for large eddy simulations. Phys. Rev. Fluids, 1(4):044401–1–26, 2016. doi:10.1103/PhysRevFluids.1.044401
  4. B. J. Geurts, A. Rouhi, and U. Piomelli. Recent progress on reliability assessment of large-eddy simulation. J. Fluids Struct., In press, available online at, 2019.
  5. O. Lehmkuhl, U. Piomelli, and G. Hozeaux. On the extension of the integral length-scale approximation model to complex geometries. Int. J. Heat Fluid Flow, 78(108422):1–12, 2019. doi:10.1016/j.ijheatfluidflow.2019.108422

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Last modified: October 2019