Section: New Results

Blood flow simulation

Simulation of Contacts without friction

Participant : Olivier Pantz.

We have developed a new contact algorithm for bodies undergoing finite deformations. Only the kinematic aspect of the contact problem has been investigated, that is the numerical treatment of the non-intersection constraint. In consequence, mechanical aspects like friction, adhesion or wear have not been considered and we restricted our analysis to the simplest frictionless case. On the other hand, our method allowed us to treat contacts and self-contacts, thin or non-thin structures in a single setting. This work has lead to the publications of two papers. One focus on the simulation of aortic valves, where complex self-contacts between the valves could occur [9] . A c++ code has been developed to treat those contacts and has been coupled with a fluid structure code by the REO team of the INRIA. The other is less specialized to a particular application and give a presentation of the algorithm in a more general setting [30] . It also contains several applications in a two dimensional case (dynamic of balloons, contacts and self-contacts between linear and non-linear elastic bodies). The codes where developed under Freefem++ and C++.

Red Blood Cells Simulation

Participant : Olivier Pantz.

Blood is essentially composed of red blood cells, white blood cells and platelets suspended in a fluid (blood plasma). If it can be considered as a homogeneous fluid when circulating in vessels of large diameter, this approximation is no longer valid when it reaches vessels with diameter of an order of magnitude comparable to that of the cells it carries. In this case, the influence of the cells on the flow can no longer be homogenized. Therefore, the mechanical behavior of red blood cells (which account for 99% of the cells presenting in the blood), their interaction with the surrounding fluid or between themselves (by contact) must be taken into account. Numerical tool plays thus an essential role: it enables to validate the advanced physical models, to access to data difficult to obtain experimentally and to determine the dependence of the flow behavior on the parameters of the model. In [24] , we proposed a numerical method which allows to take into account these three essential aspects (mechanical behavior of red blood cells, fluid/structures interactions and structures/structures contact interactions). Our study is limited to the two-dimensional case which, although simplistic, allows us to reproduce a quite large range of experimental observations as shown in the numerical simulations obtained. We intend to extend our analysis to the three dimensional case, which is a lot more difficult to tackle. In particular, both flexural and membrane effects are present in the 3d setting (whereas only flexural effects are relevant in the 2D case). Moreover, the eventual management of the meshes of the RBC and of their interaction with the fluid is also challenging.