I am using LES for my flow. I am not resolving near wall structures and hence trying to use the wall function approach, i.e. using

u/ut = 1/0.41 * ln(y*ut/nu) + 5.2

Here, u and y are the streamwise velocity and distance of the grid point nearest to the wall. nu is the kinematic viscosity.

In the above equation the only unknown is friction velocity ut:

ut = sqrt(tau_w/rho) where tau_w is the wall shear stress and rho is density

Does anyone have any experience with the methods (iterative) used to obtain ut?

Thank You.

I've seen this implementation before.. what is your specific doubt/question?

My question is does anyone have experience in the numerical method used for obtaining 'ut' iteratively?

Well, this is a transcendental equation, so the iterations here are not the conventional "algebraic iterations" but "transcendental iterations".. read up on the solution of y = log(y) and you'll know what I'm saying here. Let us know if this helps.

Well, the easiest (and probably least elegant) thing to do would be to use Newton's method on it since it can be reformulated as f(ut) = 0 (with y, nu and u as parameters). The derivative of f is easy as well. No physical reasoning there, though, and I've never personally used this myself. As I think about it, maybe it won't work after all - maybe it depends on what scheme you are using. In flows where I have used wall modeling, I "knew" ut (from other data, etc.).

I have faced the same problem before but I was dealing with RSM and not LES, the procedure is straight forward. Guess one value of Ut (on the right hand side) and iterate till you get the same value on the left hand side. You might need to use the length scale from the mixing length theory as the minimum allowable length (by using the MIN function). If you still facing problems I suggest you to consult Prof. Lars Davidson (lada@tfd.chalmers.se).