Fluid Structure Interaction Modeling in a Monolithic Frame Applied to a 2D Heart Valve Simulation

We present a fluid-structure interaction approach with applications in medicine. Fluid structure interaction problems are nowadays a subject of intensive research. The combination of mathematics and computer science, on the one hand, with bio-mechanics, chemical processes and physics, on the other hand, becomes more and more important. In this talk, we present numerical algorithms to model and simulate two-dimensional aortic heart valve dynamics. Data have been obtained by a medical doctor expert in heart valve surgery. It is known that the door from the left ventricle to the aorta consists of three valves, which implicates that a 2D simulation is not appropriate to study all physical processes. However, we are able to investigate numerical algorithms and basic effects for these kind of problems. The mathematical treatment of fluid-structure interaction is based on the so-called “arbitrary Lagrangian-Eulerian” (ALE) method, where fluid equations are rewritten in a fixed arbitrary reference domain. Afterwards, all equations for the fluid and the structure are treated in a common framework leading to an implicit solution process. We present results recently derived but also discuss numerical and mathematical challenges, for instance, how to impose appropriate boundary conditions at the outlet of the blood vessel.