Manufactured solutions for one-equation turbulence models in a two-dimensional steady wall-bounded incompressible turbulent flow

This report presents Manufactured Solutions for code and calculation verification of two-dimensional, steady, wall-bounded, incompressible, turbulent flows. The proposed solutions are specifically dedicated to one-equation models that solve a transport equations for a dependent variable that is directly related to the eddyviscosity: the one-equation models of Spalart & Allmaras and Menter. The main flow variables are identical to the ones of an existing manufactured solution. The specified flow field satisfies mass conservation, but it requires additional source terms in the momentum equations. The solutions obtained with the proposed manufactured solutions of the turbulence models dependent variable with a second-order accurate finite-difference method show that in these one-equation models it may not be easy to obtain the theoretical order of accuracy. Furthermore, the construction of the manufactured turbulence quantities as to be done carefully to avoid instabilities in the numerical solutions. The problem is model dependent: for the three manufactured solutions tested, the performance of the Spalart & Allmaras and Menter models is always different.