A hybrid subgrid-scale model constrained by Reynolds stress

Abstract

A novel constrained formulation for the dynamic subgrid-scale model for large eddy simulation (LES) is proposed. An externally prescribed Reynolds stress is used as the constraint and is imposed in the near-wall region of wall-bounded flows. However, unlike conventional zonal approaches, Reynolds stress is not imposed as the solution, but used as a constraint on the subgrid-scale stress so that the computed Reynolds stress closely matches the prescribed one only in the mean sense. In the absence of an ideal wall model or adequate near-wall resolution, a LES solution at coarse resolution is expected to be erroneous very near the wall while giving reasonable predictions away from the wall. The Reynolds stress constraint is limited to the region where the LES solution is expected to be erroneous. The Germano-identity error is used as an indicator of LES quality such that the Reynolds stress constraint is activated only where the Germano-identity error exceeds a certain threshold. The proposed model is applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions to obtain significant improvement over the dynamic Smagorinsky model, especially at coarse resolutions. This constrained formulation can be extended to incorporate constraints on the mean of other flow quantities.