Blood flow simulations can be improved by integrating known data into the numerical simulations. Data assimilation techniques based on a variational approach can have an important role on this. We will introduce a nonlinear optimal control problem to reconstruct a blood flow profile from partial observations of known data. We also propose a weighted cost function including a misfit for the wall shear stress, considered an important indicator for medical purposes.

 

Finally, we will present some numerical results for an idealized geometry, based on a discretize then optimize approach, indicating the the robustness of such a cost function with respect to different velocity profiles