Section: New Results

Fluid flow reconstruction from medical imaging

Participants : Muriel Boulakia, Miguel Ángel Fernández Varela, Felipe Galarce Marin, Damiano Lombardi, Olga Mula, Colette Voisembert.

In [22], we are interested in designing and analyzing a finite element data assimilation method for laminar steady flow described by the linearized incompressible Navier-Stokes equation. We propose a weakly consistent stabilized finite element method which reconstructs the whole fluid flow from velocity measurements in a subset of the computational domain. Using the stability of the continuous problem in the form of a three balls inequality, we derive quantitative local error estimates for the velocity. Numerical simulations illustrate these convergences properties and we finally apply our method to the flow reconstruction in a blood vessel.

In [29] a state estimation problem is investigated, that consists in reconstructing the blood flow from ultrasound Doppler images. The method proposed is based on a reduced-order technique. Semi-realistic 3D configurations are tested.