TKE Model Involving the Distance to the Wall—Part 1: The Relaxed Case

We are considering a steady-state turbulent Reynolds-Averaged Navier–Stokes (RANS) one-equation model, that couples the equation for the velocity-pressure mean field with the equation for the turbulent kinetic energy. Eddy viscosities vanish at the boundary, characterized by terms like \(d(x, \Gamma )^\eta \) and \(d(x, \Gamma )^\beta \), where \(0< \eta , \beta < 1\). We determine critical values \(\eta _c\) and \(\beta _c\) for which the system has a weak solution. This solution is obtained as the limit of viscous regularizations for \(0< \eta < \eta _c\) and \(0< \beta < \beta _c\).