How much eddy dissipation is needed to counterbalance the nonlinear production of small, unresolved scales in a large-eddy simulation of turbulence?

This paper is about models for large-eddy simulation of turbulent flow that truncate the small scales of motion for which numerical resolution is not available by making sure that they do not get energy from the larger, resolved, eddies. The resolved scales are defined with the help of a box filter. The eddy dissipation is determined in such a way that the production of too small, box-fitting, scales is counteracted. This dissipation-production balance is worked out with the help of Poincare's inequality, which results in a condition that depends on the invariants of the velocity gradient. If the filter box is anisotropic the truncation condition is to be scaled in order to account for the anisotropy in the right way. The scaled truncation condition is applied to an eddy-viscosity model. This model is discretized and equipped with a Schumann filter. It is successfully tested for homogeneous turbulence as well as for turbulent channel flow. (C) 2016 Elsevier Ltd. All rights reserved.