A New Subgrid Characteristic Length for LES

  • F. X. TriasEmail author
  • A. Gorobets
  • A. Oliva
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 25)


Large-eddy simulation (LES) equations result from applying a spatial commutative filter, with filter length \(\varDelta \), to the Navier–Stokes equations
$$\begin{aligned} \partial _t \overline{\varvec{u}} + \left( \overline{\varvec{u}} \cdot \nabla \right) \overline{\varvec{u}} = \nu \nabla ^2\overline{\varvec{u}} - \nabla \overline{p} - \nabla \cdot \tau ( \overline{\varvec{u}} ) , \quad \nabla \cdot \overline{\varvec{u}} = 0, \end{aligned}$$
where \(\overline{\varvec{u}}\) is the filtered velocity and \(\tau (\overline{\varvec{u}})\) is the subgrid stress (SGS) tensor and aims to approximate the effect of the under-resolved scales, i.e. \(\tau (\overline{\varvec{u}} ) \approx \overline{\varvec{u}\otimes \varvec{u}} - \overline{\varvec{u}} \otimes \overline{\varvec{u}}\). Most of the difficulties in LES are associated with the presence of walls where SGS activity tends to vanish. Therefore, apart from many other relevant properties, LES models should properly capture this feature [1].



This work has been financially supported by the Ministerio de Economía y Competitividad, Spain (ENE2017-88697-R), and a Ramón y Cajal postdoctoral contract (RYC-2012-11996). Calculations have been performed on the IBM MareNostrum supercomputer at the Barcelona Supercomputing Center. The authors thankfully acknowledge these institutions.


  1. 1.
    Trias, F.X., Folch, D., Gorobets, A., Oliva, A.: Building proper invariants for eddy-viscosity subgrid-scale models. Phys. Fluids 27(6), 065103 (2015)CrossRefGoogle Scholar
  2. 2.
    Chapman, D.R.: Computational aerodynamics development and outlook. AIAA J. 17(12), 1293–1313 (1979)CrossRefGoogle Scholar
  3. 3.
    Choi, H., Moin, P.: Grid-point requirements for large eddy simulation: chapman’s estimates revisited. Phys. Fluids 24(1), 011702 (2012)CrossRefGoogle Scholar
  4. 4.
    Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62(3), 183–200 (1999)CrossRefGoogle Scholar
  5. 5.
    Vreman, A.W.: An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16(10), 3670–3681 (2004)CrossRefGoogle Scholar
  6. 6.
    Verstappen, R.: When does eddy viscosity damp subfilter scales sufficiently? J. Sci. Comput. 49(1), 94–110 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Nicoud, F., Toda, H.B., Cabrit, O., Bose, S., Lee, J.: Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23(8), 085106 (2011)CrossRefGoogle Scholar
  8. 8.
    Deardorff, J.W.: Numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480 (1970)CrossRefGoogle Scholar
  9. 9.
    Trias, F.X., Gorobets, A., Silvis, M.H., Verstappen, R.W.C.P., Oliva, A.: A new subgrid characteristic length for turbulence simulations on anisotropic grids. Phys. Fluids 29(11), 115109 (2017)CrossRefGoogle Scholar
  10. 10.
    Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, isotropic turbulence. J. Fluid Mech. 48, 273–337 (1971)CrossRefGoogle Scholar
  11. 11.
    Trias, F.X., Gorobets, A., Oliva, A.: A simple approach to discretize the viscous term with spatially varying (eddy-)viscosity. J. Comput. Phys. 253, 405–417 (2013)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Heat and Mass Transfer Technological Center, Technical University of CataloniaTerrassaSpain
  2. 2.Keldysh Institute of Applied MathematicsMoscowRussia

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