Statistically invariant eddy viscosity models

Abstract

We presently generalize existing two-equation Reynolds-averaged Navier–Stokes models by using recent advances in our understanding of the Lie symmetries of governing turbulence. The motivation for this and the necessary steps are laid out using the conventional terminology of turbulence modeling, without requiring deep knowledge about the mathematical concept of symmetries. For illustration purposes, these steps are applied to the standard k–ε model and the k–ω model. The so-modified k–ε model is applied to a wide range of canonical flows. For all of them, it is shown to match or even improve the performance of its classical counterpart and is, thus, shown to be more general than the original k–ε model.