@TechReport{	  it:2017-005,
  author	= {Saleh Rezaeiravesh and Mattias Liefvendahl},
  title		= {Grid Construction Strategies for Wall-Resolving Large Eddy
		  Simulation and Estimates of the Resulting Number of Grid
		  Points},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2017},
  number	= {2017-005},
  month		= apr,
  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 $\mathcal{O}(10^2)$, which relaxes to up to
		  $\mathcal{O}(10)$ for fully-developed turbulent channel
		  flow.}
}