Grid construction strategies for wall-resolving large eddy simulation and estimates of the resulting number of grid points

Estimates of the total number of grid points required for wall-resolving large eddy simulation (WR-LES) of canonical wall-bounded turbulent flows, corresponding to different grid
construction strategies, are derived. The common basis for all strategies is that the first
off-wall grid spacing is of the order of the local viscous length scale. First, the estimate of
the number of grid points for the block-nested grids, which are widely used in literature to
calculate the computational cost of WR-LES, is reviewed in a general setting. Then, different functions, with appropriate controlling parameters, are introduced for distributing the
grid points in the wall-normal direction. By using these functions along with assuming grid
spacings in the streamwise and spanwise directions to be independent of the wall-normal
coordinate, block-structured grids can be constructed, for which analytical expressions are
derived to show the dependency of the total number of grid points to the flow Reynolds
number. It is shown that under equivalent conditions, this class of grids demands more
grid points than the block-nested ones. In particular, for a zero-pressure-gradient turbulent
boundary layer at high Reynolds numbers, the increase in the number of grid points can be
up to O(102
), which relaxes to up to O(10) for fully-developed turbulent channel flow