Wall Function for LES

Hello Guys,

Although there’re several papers discussing the wall function for LBM-LES simulations. However, I still can’t understant it.

van-Driest model

In Premnath, Pattison’s paper (PRE, 2009, 79: 026703), the turbulence filter size is tuned according to
\Delat = \delta x [1 - exp(z+ / A+)],
where A+ is a constant, and z+ depends on the “shear stress” in the boundary layer. Both z+ and A+ are dimensionless.

The \Delta is further used to estimate the turbulence viscosity.

The question is how to estimate the “shear stress” here - JUST use the velocity neighboring to the wall. And use the \bar(u) / z? Where, z is the normal distance between the grid point and the wall.