Olivier Pironneau est professeur émérite au Laboratoire Jacques-Louis Lions de l'université Pierre et Marie Curie, Paris 6. Il est invité à parler au séminaire du laboratoire MAS coencadré par la Fédération de Mathématiques de CentraleSupélec.
Titre : Contribution à l'identification des paramètres pour les problèmes d'interaction fluide-structure.
Résumé :
Is it possible to recover the parameters of a fluid-structure system in interaction from images of the system? Is the system observable? What are the algorithms available for identification?
An important application is for hemodynamics and the identification of the blood rheology and the blood vessel’s mechanical parameters from MRI images.
Our contribution to this field is the study of a reduced fluid-structure interaction algorithm for the Navier-Stokes equation coupled with a shell model. By using transpiration condition the model runs easily on a laptop computer. It has also been fully analyzed mathematically and shown to be well posed and stable after discretization.
Calculus of variations and control theory provides a framework to implement a 4D-var parameter identification algorithm. We will discuss the discretization schemes and the implementation with finite element methods and descent methods.