A rational length scale for large-eddy simulation of turbulence on anisotropic grids

Abstract: Due to the prohibitive cost of resolving all relevant scales, direct numerical simulations of turbulence remain unfeasible for most real-world applications. Consequently, dynamically simplified formulations are needed for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are widely used both in academia and industry. These models require a subgrid characteristic length, typically linked to the local grid size. While this length scale corresponds to the mesh step for isotropic grids, its definition for unstructured or anisotropic Cartesian meshes, such as the pancake-like meshes commonly used to capture near-wall turbulence or shear layers, remains an open question. Despite its significant influence on LES model performance, no consensus has been reached on its proper formulation. In this work, we introduce a novel subgrid characteristic length. This length scale is derived from the analysis of the entanglement between the numerical discretization and the filtering in LES. Its mathematical properties and simplicity make it a robust choice for reducing the impact of mesh anisotropies on simulation accuracy. The effectiveness of the proposed subgrid length is demonstrated through simulations of decaying isotropic turbulence and a turbulent channel flow using different codes.