We review the optimal design of an arterial bypass graft following either a (i) boundary
optimal control approach, or a (ii) shape optimization formulation. The main focus is
quantifying and treating the uncertainty in the residual flow when the hosting artery is
not completely occluded, for which the worst-case in terms of recirculation effects is
inferred to correspond to a strong orifice flow through near-complete occlusion.A
worst-case optimal control approach is applied to the steady Navier-Stokes equations in 2D
to identify an anastomosis angle and a cuffed shape that are robust with respect to a
possible range of residual flows. We also consider a reduced order modelling framework
based on reduced basis methods in order to make the robust design problem computationally
feasible. The results obtained in 2D are compared with simulations in a 3D geometry but
without model reduction or the robust framework.