### Technical Report 2017-005

# Grid Construction Strategies for Wall-Resolving Large Eddy Simulation and Estimates of the Resulting Number of Grid Points

### Saleh Rezaeiravesh and Mattias Liefvendahl

April 2017

**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**(10^{2}), which relaxes to up to **O**(10) for fully-developed turbulent channel flow.

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