convergence of Spalart-Allmaras and k-w(SST) turbulence models
 

dear friends,
now i'm attempting to simulate 3D Navier-Stokes equations with one-equation (S-A) and/or two-equation (k-w SST) turbulence models using JST scheme coupled implicit LU-SGS method. even found some papers related to its positive and convergence about the models, it is hard to obtain an convergent steady result. under some conditions when very small CFL number was adopted, the simulation may be stable. so i have two main problems here:
1. the stability of numerical method to solve turbulence governing equations: explicit vs implicit; CFL number
2. how great/small the turbulent viscosity is satisfied: the lower value limiter; initial values

hope to receive your reply. do appreciate for your attention!