How to do the wall boundary conditions for γ-Reθt transition model?
 

I want to use the γ-Reθt model for the prediction of hypersonic flow, but I do not know how to do the wall boundary conditions for γ and Reθt.

According to Langtry and Menter’s paper “R.B. Langtry, F. R. Menter, Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes, AIAA Journal, 2009, 47(12):2894-2906”, the boundary conditions for γ and Reθt at a wall are zero normal flux and zero flux, respectively.

I think the normal fluxes of γ and Reθt are ρVnγS and ρVnReθtS, respectively, where the ρ, Vn and S are density, normal velocity and wall area of a control volume, respectively. Because the velocity Vn is zero at the no-slip wall, ρVnγ and ρVnReθt are zero regardless of the values of γ and Reθt.

I have read a lot of papers about the transition prediction with γ-Reθt transition model. There are two methods about the boundary conditions of γ and Reθt. Some set the γ and Reθt as zero at the wall, and others set the normal gradients of γ and Reθt as zero at the wall. Which method is the better choice? Or if is any other method better?