@TechReport{	  it:2017-001,
  author	= {Mattias Liefvendahl and Timofey Mukha and Saleh
		  Rezaeiravesh},
  title		= {Formulation of a Wall Model for {LES} in a Collocated
		  Finite-Volume Framework},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2017},
  number	= {2017-001},
  month		= jan,
  abstract	= {Wall-modelled Large-Eddy Simulation (WMLES) is a
		  turbulence modelling approach that aims to reduce the
		  computational costs of traditional (wall-resolved) LES by
		  introducing special treatment of the near-wall region. In
		  this report, a detailed derivation is given of a widely
		  used wall model which is based on implicitly enforcing the
		  correct local wall shear stress. The model is developed in
		  the framework of a collocated finite volume method, with
		  unstructured meshes and arbitrary polyhedral grid cells.
		  The expression for the law of the wall proposed by Spalding
		  is used to relate the finite volume cell flow velocity to
		  the wall-shear stress. The computational cost and
		  predictive accuracy of the overall method is evaluated by a
		  series of turbulent channel flow simulations covering a
		  range of Re-numbers, from $10\,000$ to $125\,000$, based on
		  the bulk velocity and channel half-height. For validation,
		  the WMLES-results are compared to publicly available
		  results from direct numerical simulations. It is
		  demonstrated that the WMLES approach significantly reduces
		  the computational cost, as compared to wall-resolved LES,
		  while maintaining an acceptable accuracy of, at least,
		  first-order statistical moments of the unknowns.}
}