Grid requirements for hybrid LES/RANS

Outside of the near wall region intended to be modeled as pure RANS, the grid requirements for a wall-modeled hybrid RANS/LES are essentially identical to what would be required for LES. The required grid resolution depends on the dissipative nature of the numerical schemes that are employed. Given this fact, the guidelines that follow will assume a low-dissipation numerical framework utilizing either high-order finite differences with non-dispersive filters or hybrid high-order dissipative/non-dissipative operators (in either a finite volume or finite difference context). The vast majority of high quality hybrid RANS/LES applications documented in the literature invoke a numerical framework from one of these classes.

Given that the inner portion of the wall region is modeled with RANS, and that most of the turbulence energy in the outer portion of the boundary layer resides in the larger eddies that scale with the height of the boundary layer, it is natural to design grids with spacings measured as a fraction of the boundary layer height. Experience has shown that 10 to 20 cells (per boundary layer thickness) are needed in the streamwise direction, while 15 to 25 cells are required in the spanwise direction. The wall normal direction has requirements driven both by RANS demands near the wall and LES demands in the outer portion of the boundary layer. The use of RANS as a near-wall closure model requires a wall spacing that corresponds to a non-dimensional boundary layer wall unit (y+) of 1 or less, while the use of LES in the outer portion dictates a wall normal spacing that should be on the order of the streamwise and spanwise grid spacings. As a result, the wall normal spacing near the edge of the boundary layer is typically set equal to the spanwise spacing with the wall-normal grid stretch rate limited to 10% or less. It should be emphasized that these guidelines are only meant to guide the design of a grid that has the potential to be suitable for wall-modeled LES usage. The appropriateness of the final grid used for this purpose can only be ascertained through a posteriori grid sensitivity studies.