Date & Time: Monday, January 20, 2014, 14:30-15:30.
Venue: Ramanujan Hall
Speaker: Olivier Pironneau, University of Paris VI
Title: Some Computational Problems of Hemodynamics
Abstract: Simulations of blood flows in arteries require numerical solutions of fluid-structure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessel.
Among the various simplifications which have been proposed, the surface pressure model can be analyzed fully. It exhibits fundamental frequencies which can be analyzed and compared with the pulse. Consequently we can derive unconditionally stable time discretizations by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls can be decomposed and Rannacher's scheme is the fastest computationally.
Next we will propose outflow conditions appropriate to connect the computational domain with the rest of the circulatory system; we shall show numerically that viscous buffer zones work efficiently and discuss the numerical implementation with the software freefem++.
The talk will also be an opportunity to review the literature and the known results.