This work presents the preliminary verification and validation of the SSG/LRR-ln \((\omega )\) Reynolds stress model (RSM) in the flow solver CODA. First, we describe the verification of the implementation and the model validation for turbulent boundary layer and airfoil flows. Then we study the robustness within the implicit numerical solution scheme used in CODA and its convergence behaviour through the numerical simulations of two dimensional turbulent boundary layer flows and airfoil flows. Different convergence criteria are considered i.e., convergence of the residual and Cauchy-convergence of surface quantities. Violation of realizability constraints for the Reynolds stresses is found to cause robustness issues. In the present context of an implicit solution scheme, classical clipping strategies cannot be applied, and hence different alternative methods to ensure realizability are studied. Best robustness improvement is found by non-linear positivity filters, which are used during the transient phase for steady state problems and then deactivated to achieve full residual convergence.