Grid-adaptation in large eddy simulation: finding the optimal filter-width as a function of space and direction

The grid is the single most important factor determining the accuracy of a large eddy simulation, controlling both the numerical errors and the errors due to the modeling of the unresolved scales. The simultaneous dependence of both numerical and modeling errors on the grid resolution makes finding the optimal grid more complicated than in DNS or RANS, where the grid only controls the numerical errors. The purpose of the present study is to introduce an efficient technique that eliminates or reduces the need for input from user's knowledge of turbulence in grid generation, is capable of producing optimal unstructured grids with varying resolution in space and direction, and that is still practical for generating LES grids in realistic settings. The proposed method is tested on turbulent channel flow (where the optimal grid is relatively well known) and on the flow over a backward-facing step, which has a more complex flow that requires a grid with varying resolution in space and different optimal aspect ratios in each location. The proposed method performs well in both test cases and produces nearly optimal grids.