Resolution-induced anisotropy in large-eddy simulations

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.