## Abstract

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

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

Original language | English |
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Publication status | Published - Apr 2017 |