
Here you are the first results of the SEM method in a simple channel flow. The simulation run, even if was just a try (so was run with just a coarse grid with the followings dimensions 20 x 2 x 3.5, and this cell division 40 x 20 x 20), is very usefull regardless. We are able to understand in a better way how to improve the standard SEM method (improvements that might be usefull for the DFSEM too).
Here I plot the SEM inlet (upper image) and the LES outlet (lower one). Even from just these two images we can understand that the SEM method needs to have a kind of "boundary condition implementation".
The SEM I used to generate this inlet has the following form for %$ \sigma $% %reflatex{eq:Sigma}%
Since the SEM version I implemented is a slightly modified version that consider a direction and velocity dependence of %$ \sigma $% as showed in %reflatex{eq:Sigmaij}%
%BEGINLATEX{label="eq:Sigma"}%\begin{equation*} \sigma = MAX(min(\frac{k^{\frac{3}{2}}}{\epsilon},\kappa \delta),\Delta),~~~~\Delta = MAX(\Delta x, \Delta y, \Delta z) ~~~~~~~~~ \end{equation*}%ENDLATEX% 
%BEGINLATEX{label="eq:Sigmaij"}%\begin{equation*} \sigma = \sigma_{ij} ~~~~ used~ for~ each~ velocity~ component~ i~ and~ each~ direction~ j~ \end{equation*}%ENDLATEX% 
The main difference in the method implemented are the "shapes" of eddies.It is easier to show in a pseudocode how I implemented this feature, presents in Jarrain thesis.

Nicolas, in his thesis, run several channel flow and many others different geometry. Actually, the expression used for %$ \sigma $% in %reflatex{eq:Sigma}% is the one that Nicolas used in a "general RANSLES coupling", and is based on the hypothesis that %$ \sigma_{ij} = \sigma $%, that is constant in all directions and velocity components.
Actually Nicolas used once a different specification for each component of %$ \sigma $% tensor in one channel flow. He defined it in the following way:
%$ \sigma_{i2} = \sigma_{i3} $% %$ \sigma_{i3} = $% defined from a previous LES periodic channel flow, as the distance at which the twopoint correlations drop to 0.1 %$ \sigma_{i1} = U_c T_i $% where %$ U_c $% is the average velocity and %$ T_i $% is a timescale, calculated again from a previous LES periodic channel flow 
The implementation of a boundary condition in the SEM method should not be so difficult. In fact, considering a simple channel flow, the only condition to be satisfied is the following: %$ v' = 0 $%. Since, considering the %reflatex{eq:Sigmaij}% the v' component is:
%BEGINLATEX{label="eq:vprimo"}%\begin{equation*} v' = K \frac{(\sigma_{12}\alpha)(\sigma_{22}\beta)(\sigma_{32}\gamma)}{\sqrt{\sigma_{12} \sigma_{22} \sigma_{32}} (\sigma_{12} \sigma_{22} \sigma_{32}) } \end{equation*}%ENDLATEX%
%BEGINLATEX{label="eq:vprimoDEF"}%\begin{equation*} \alpha = \mathbf{X}point_1  \mathbf{X}eddy_1, \beta = \mathbf{X}point_2  \mathbf{X}eddy_2, \gamma = \mathbf{X}point_2  \mathbf{X}eddy_2, \end{equation*}%ENDLATEX%
A logical way to implement a kind of boundary condition in the SEM method could be a modification in the eddy box. So far this box is defined by the following relations %$ x_{i,min} = \underset{min}{x \in S}(x_i  \sigma(\mathbf{x})) ~~~~~~~~ x_{i,max} = \underset{max}{x \in S}(x_i + \sigma(\mathbf{x})) $%.
In a real case the turbulence applies only in a region which does not include the viscous sublayer. Could be interesting then to limit the SEM method only to a zone with %$ y^+ > 5 \div 30 $% (I think that a lower limit is better because of the random eddies positions, which need a kind of buffer region to be fully developed). This allow us to be in the loglaw area, where turbulence is fully developed.
Serial in MAN2E 
Parallel (2 processors) in MAN2E 
Parallel (8 processors) in MAN2E 
Serial in my own PC 