Detailed investigation of subgrid scale models in large-eddy simulation using high aspect-ratio grid spacing

In large eddy simulation (LES), we generally use information of the grid width in representing a filter width (Δ) to evaluate a subgrid scale (SGS) model. In practical applications, however, the grid widths are largely different in the streamwise and cross-streamwise directions, resulting in grid cells having high aspect ratios. In such a case, we often adopt the cube root of the grid-cell volume for the filter width; i.e., Δ = (Δ x Δ y Δ z)1/3 in the Cartesian grid system. Although this has been regarded as a standard way to determine the filter width, its superiority over other strategies, such as using the maximum width in all directions (i.e., Δ = max (Δ x, Δ y, Δ z)), has not always been made clear. In this paper, to investigate the effect of the definition of a filter width on the prediction accuracy of an SGS model, we report on a priori tests of several SGS models using highly resolved LES data of a backward-facing step flow. We focus particularly on the model performance in the shear layer downstream of a step, where there exists a strong velocity gradient and the aspect ratio of a grid cell is high despite the region being far from wall surfaces. This investigation enables us to distinguish the effect of the grid aspect ratio from that of near-wall damping. We make the important finding that the cube root of a grid-cell volume is not always appropriate for the filter width. To evaluate an SGS model properly, the effect of a grid width in one direction much smaller than in other directions must be excluded in determining the filter width.