Direct and Large-Eddy Simulation XI pp 135-141 | Cite as
A New Subgrid Characteristic Length for LES
Conference paper
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Abstract
Large-eddy simulation (LES) equations result from applying a spatial commutative filter, with filter length \(\varDelta \), to the Navier–Stokes equations 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].
$$\begin{aligned} \partial _t \overline{\varvec{u}} + \left( \overline{\varvec{u}} \cdot \nabla \right) \overline{\varvec{u}} = \nu \nabla ^2\overline{\varvec{u}} - \nabla \overline{p} - \nabla \cdot \tau ( \overline{\varvec{u}} ) , \quad \nabla \cdot \overline{\varvec{u}} = 0, \end{aligned}$$
Notes
Acknowledgements
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.
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