Hickel, S., Adams, N.A., Mansour, N.N. (2007)
Physics of Fluids 19: 095102.  doi: 10.1063/1.2770522

Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The name “implicit LES” is used for approaches that merge the SGS model and numerical discretization.

In this paper, the implicit SGS modeling environment provided by the adaptive local deconvolution method is extended to LES of passive-scalar mixing. The resulting adaptive advection algorithm is discussed with respect to its numerical and turbulence-theoretical background. We demonstrate that the new method allows for reliable predictions of the turbulent transport of passive scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers.


Critical test cases for predicting the proper subgrid diffusion in large-eddy simulations of scalar mixing. Top: Low-Schmidt-number regime. Bottom: High-Schmidt-number regime at moderate Reynolds number. ––––– scalar variance; kinetic energy; numerical cutoff wavenumber.


Mean 3-D spectra of kinetic energy and scalar variance for implicit LES of large-scale forced isotropic turbulence. Top: Re=104 and Sc=1. Bottom: Re=20 and Sc=400. ––––– scalar variance; – – – – kinetic energy; ∙∙∙∙∙∙ analytical scaling law for scalar variance.


Mass transfer coefficient 𝐾+ for channel flow at Re𝜏=180: 𝛥 implicit LES with parameters for low Schmidt numbers, ▿ implicit LES with parameters for high Schmidt numbers, ∘ DNS (Ref. 33), ◇ semi-DNS (Ref. 34). ◻ 𝐾+ for Lagrangian DNS (Ref. 35) of channel flow at Re𝜏=150. × 𝐾+ for LES of channel flow at Re𝜏=640 using the dynamic mixed SGS model (Ref. 36). Lines denote curve fits of Shaw and Hanratty (Ref. 37) to experimental data for turbulent pipe flow: ∙–∙–∙– 𝐾+=0.0649Sc−2∕3, – – – – 𝐾+=0.0889Sc−0.704.