Miguel A. Fernández (Inria Paris-Rocquencourt and Université Paris VI, France).
Mathematical models describing the mechanical interaction of an incompressible viscous fluid with a thin-walled flexible structure appear in a wide variety of engineering fields: from micro-encapsulation to the aeroelasticity of parachutes and sailing boats. Such multi-physics systems are also particularly ubiquitous in nature.
One can think, for instance, of the wings of a bird interacting with the air, the fins of a fish moving through the water, or the opening/closing dynamics of heart valves when blood is propelled into the arteries. The solid is deformed under the action of the fluid and the fluid flow is disturbed by the moving solid. These problems are generally modeled by non-linear heterogeneous (parabolic/hyperbolic) systems of equations with an interface coupling which can be extremely stiff (the so-called added-mass effect). This often compromises the efficiency of the time-stepping.
Moreover, in the case of immersed solids, the thin-walled nature of the structure introduces weak and strong discontinuities of the velocity and pressure fields which might deteriorate the accuracy of the spatial approximation.
In this talk, we will present some recent results on the development of efficient and accurate numerical methods for of these coupled systems.