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. © EDP Sciences, SMAI 2013.
|Titolo:||Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty|
|Autori:||Lassila, T; Manzoni, A; Quarteroni, A; Rozza, G|
|Rivista:||MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1051/m2an/2012059|
|Fulltext via DOI:||10.1051/m2an/2012059|
|Appare nelle tipologie:||1.1 Journal article|