A heuristic argument for the sole use of numerical stabilization with no physical LES modeling in the simulation of incompressible turbulent flows

Abstract

We aim at giving support to the idea that no physical Large Eddy Simulation (LES) model should be used in the simulation of turbulent flows. It is heuristically shown that the rate of transfer of subgrid kinetic energy provided by the stabilization terms of the Orthogonal Subgrid Scale (OSS) finite element method is already proportional to the molecular physical dissipation rate (for an appropriate choice of the stabilization parameter). This precludes the necessity of including an extra LES physical model to achieve this behavior and somehow justifies the purely numerical approach to solve turbulent flows. The argumentation is valid for a fine enough mesh with characteristic element size, $h$, so that $h$ lies in the inertial subrange of a turbulent flow.