Impact of anisotropic subgrid-scale stress in wall-modeled large-eddy simulation of flow over a Gaussian bump

We investigate a posteriori the role of anisotropic subgrid-scale (SGS) stress in wall-modeled large-eddy simulation of flow over a Gaussian-shaped bump. Our simulations show that eddy-viscosity-based SGS models often yield nonmonotonic predictions of the separation bubble size on the leeward side under grid refinement, whereas models incorporating anisotropic SGS stress produce more consistent results across resolutions. To identify where SGS anisotropy becomes critical, we design a numerical experiment that applies different SGS models to the upstream and downstream regions of the domain, separated by a virtual interface. This experiment indicates that the upstream region, particularly near the bump peak where a strong favorable pressure gradient exists, is crucial in determining downstream flow separation. A budget analysis of the resolved Reynolds stress transport equation in this region reveals that anisotropic SGS stress directly modifies the resolved Reynolds stress in the boundary layer, thereby influencing the mean momentum and pressure gradient near the bump peak. At coarse resolutions, the mean SGS stress dominates the momentum distribution, and the differences between the eddy-viscosity-based SGS model and the anisotropic model are minor. However, as the mesh is refined, the resolved Reynolds stress within the boundary layer becomes more significant, and the influence of anisotropic SGS stress leads to noticeable differences in the downstream flow, including changes in the mean velocity profile and the size as well as location of the separation bubble.