The Zonal Two-layer Approach
The objective of the zonal strategy is to provide the LES region with the wall-shear stress, extracted from a separate modelling process applied to the near-wall layer. The wall-shear stress can be determined from an algebraic law-of-the-wall model or from differential equations solved on a near-wall-layer grid refined in the wall-normal direction - an approach referred to as two-layer wall modelling. The method was originally proposed by Balaras and Benocci and tested by Tessicini et al. At solid boundaries, the LES equations are solved up to a near-wall node which is located, typically, at 
. From this node to the wall, a refined mesh is embedded into the main flow,and the following simplified turbulent boundary-layer equations are solved:
![\frac{\partial{\rho\tilde{U}_i}}{\partial{t}}+ \frac{\partial{\rho\tilde{U}_i\tilde{U}_j}}{\partial{x_j}}+ \frac{d\tilde{P}}{dx_i} = \frac{\partial}{\partial{y}}[(\mu+\mu_t)\frac{\partial{\tilde{U}_i}}{\partial{y}}]\quad i=1,3](http://www.cfd-online.com/W/images/math/826c62fcb6d1a67d374b926431941843.png)
where y denotes the direction normal to the wall and i identify the wall-parallel directions (1 and 3).
The eddy viscosity 
is obtained from a mixing-length model with near-wall damping, as done by Wang and Moin : 
The boundary conditions for the turbulent boundary layer equations are given by the unsteady outer-layer solution at the first grid node outside the wall layer and the no-slip condition at y=0.
References:
Balaras E. and Benocci C. (1994) In: Applications of Direct and Large Eddy Simulation, AGARD. pp. 2-1-2-6.
Cabot W. and Moin P. (2000) Flow, Turbulence and Combustion, 63:269-291
Tessicini F., Temmerman L. and Leschziner M.A. (2005) In: 6th Engineering Turbulence Modelling and Measurements (ETMM6)
posted by fabrizio at 1:30 AM
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