LES approach coupled with stochastic forcing of subgrid acceleration in a high-Reynolds-number channel flow

Abstract

In this paper, the high-Reynolds-number channel flow is simulated by numerical approach at coarse resolution, in which the instantaneous acceleration is decomposed into filtered and subgrid parts, and then both components are modeled. The filtered acceleration is modeled in the framework of the large-eddy simulation approach. The model for the subgrid acceleration is based on two stochastic processes. The first is for its norm and is based on statistical universalities in fragmentation under scaling symmetry, providing correlation of subgrid forcing across the channel. The second is for its orientation and is based on the Brownian motion on a unit sphere in order to represent a stochastic relaxation toward full isotropy away from the wall. Two main parameters of the stochastic process include the Reynolds number based on the friction velocity and the channel half-width. In order to assess the capability of the model proposed, the paper illustrates its application versus recent high-Reynolds-number direct numerical simulations, including direct numerical simulations performed in this paper.

Keywords:

• Turbulent channel flow
• intermittency
• large-eddy simulation
• subgrid-scale model

Acknowledgments

M. Buffat is acknowledged for the development of the computational code. The authors express their gratitude to F. Laadhari who kindly provided his initial fields for the DNS. It is a pleasure to thank V. Sabel'nikov, P. Moin, and J. Jiménez for discussions on this subject with many benefits for us. This work was granted access to the High Performance Computing resources of Centre Informatique National de l'Enseignement Supérieur under the allocation 2009-c200902560 made by Grand Equipement National de Calcul Intensif.

Notes

^a dt ⁺=dt/t _* is the time step of the simulation; t _*=ν/u _* ² is a viscous time of the order of the Kolmogorov time scale at the wall.

^a[47].

^a[48].