Derivation of a new LES model approximated from exact two-point equations and evaluation in a Taylor-Green flow
Phys. Rev. Fluids 11, 014607 – Published 28 January, 2026
DOI: https://doi.org/10.1103/pkyq-vtd6
Abstract
The Kármán-Howarth-Monin-Hill equation has been used by various authors to quantify and understand the small-scale turbulent energy cascade without assumptions and therefore even in the case of nonhomogeneous turbulence. A complementary equation was introduced by Germano [Germano et al., Phys. Fluids 19, 038102 (2007)] to describe the large-scale dynamics of the flow. In this paper, the links between the Germano equation and large-eddy simulation (LES) are examined and an approximation of an exact equation is used to design a new LES model which captures the physical energy transfer between filtered scales and residual subfilter scales. This new model, based on simple simplifications of exact equations, is tested both a priori and a posteriori in a Taylor-Green flow. The model is found to better represent the local energy transfers compared to a similar model introduced by Brun [Brun et al., Theor. Comput. Fluid Dyn. 20, 1 (2006)], especially for both extreme forward and backscatter events. The Bardina et al. scale similarity model [Bardina et al., AIAA 80, 1357 (1980)] overperforms our model in the a priori analysis, meaning that refining the mathematical approximations used for the derivation of our model could be useful, but our model's performance is comparable to, if not even better than, the scale similarity model in a mixed configuration, including a turbulent viscosity model. Therefore, our model, derived with simple simplifications of the exact two-point equations, already performs similarly to the LES models classically used for simulations. This paper provides a proof of concept that two-point equations can be used to develop new LES models and it may be the right direction to develop more efficient models derived from the Navier-Stokes equations.
