Optimal Control problems of NS-α and NS-ωturbulencemodels: analysis and numerical tests

In this study, optimal control problems for the Navier-Stokes-alpha(NS-alpha) model andthe Navier-Stokes-omega(NS-omega) model are considered. Optimality conditions are derived,and semi-discrete a priori error estimates for all fluid variables are analyzed for bothmodels. Numerical tests are performed to verify the accuracy of the theoretical findingsand to demonstrate the effectiveness of optimal control. Given the proven utility ofthe NS-alpha and NS-omega models in fluid dynamics, this study addresses a significant gapby exploring the potential of optimal control to enhance the performance, efficiency,safety, and environmental impact of fluid systems.