# Resolution-induced anisotropy in LES

## TL;DR

This paper investigates how anisotropic resolution in LES affects turbulence modeling, revealing that common models perform poorly under such conditions, and introduces a new anisotropic eddy diffusivity model that depends only on turbulence statistics.

## Contribution

The paper demonstrates the impact of resolution-induced anisotropy on LES turbulence statistics and proposes a novel anisotropic eddy diffusivity model based solely on turbulence dissipation rate.

## Key findings

- Anisotropic resolution induces Reynolds stress and velocity gradient anisotropy.
- Most existing subgrid models perform poorly with anisotropic resolution.
- The proposed model performs well and depends only on turbulence dissipation rate.

## Abstract

Large eddy simulation (LES) of turbulence in complex geometries and domains is often conducted with high aspect ratio resolution cells of varying shapes and orientations. The effects of such anisotropic resolution are often simplified or neglected in subgrid model formulation. Here, we examine resolution induced anisotropy and demonstrate that, even for isotropic turbulence, anisotropic resolution induces mild resolved Reynolds stress anisotropy and significant anisotropy in second-order resolved velocity gradient statistics. In large eddy simulations of homogeneous isotropic turbulence with anisotropic resolution, it is shown that commonly used subgrid models, including those that consider resolution anisotropy in their formulation, perform poorly. The one exception is the anisotropic minimum dissipation model proposed by Rozema et al. (Phys. of Fluids 27, 085107, 2015). A simple new model is presented here that is formulated with an anisotropic eddy diffusivity that depends explicitly on the anisotropy of the resolution. It also performs well, and is remarkable because unlike other LES subgrid models, the eddy diffusivity only depends on statistical characteristics of the turbulence (in this case the dissipation rate), not on fluctuating quantities. In other subgrid modeling formulations, such as the dynamic procedure, limiting flow dependence to statistical quantities in this way could have advantages.