Anisotropic grid-adaptation in large eddy simulations

Grid-adaptation requires an error indicator that identifies where and how the grid should be refined. In the case of turbulence-resolving simulations (LES, DNS, etc), a simple and intuitive error indicator is the small-scale energy which can be linked to both the modeling errors and the numerical errors. The purpose of this work is to introduce a new error indicator for large eddy simulations that is based on the small-scale energy in a directional manner, i.e., in a way that enables anisotropic grid-adaptation. The formulation is geometrically general and applicable to arbitrary geometries and grid topologies. The error indicator is first assessed on turbulent channel flow to test its ability to predict the optimal anisotropy of the grid, and then assessed on the flow over a backward-facing step to test its performance in a more complex case with an unstructured grid.